Wolfgang WOESS

Institut für Diskrete Mathematik
Technische Universität Graz
Steyrergasse 30
8010 Graz, Austria

phone: ++43 (0)316 873-7130
fax: ++43 (0)316 873-4507
email: woess[at]TUGraz[dot]at


W.W. by Vadim

I am deeply ashamed of the attitude of the Austrian
government towards the fate of the refugees on
the Greek island of Lesbos. Particularly shocking were
the disgusting statements of the ministers Schallenberg
(foreign affairs) and Nehammer (interior), and the
subsequent one of chancellor Kurz appealing to his
"conscience". I wish those guys would get themselves
locked in a kind of human pressure cooker along with
some thousand of their right wing party members. With
the heat turned on under the cooker, it is bound to
explode, unless someone lets off the steam. Would they
stay peaceful and obedient in that situation? In reality,
this serves to maximise transfer votes from the extreme right
"Freedom party" in the forthcoming Vienna regional election.
The Green party's role in the government has been a
failure in many respects.



- About myself
- Research interests
- FWF projects
- Books
- Papers
- Conferences
- Coauthors
- Refereeing
- Teaching
- Politics
- True stories
- F.Woess (1915-1995),
- E.Woess (1917-2001)
- Photography by W.W.

Since May, 2010, we are running a doctoral program (DK = Doktoratskolleg) financed primarily by the Austrian Science Fund (FWF), and also by TU and KFU Graz. This is a joint effort of mathematicians at Technische Universität Graz, Karl Franzens Universität Graz and Montanuniversität Leoben. I am the speaker of this large project. The funding is substantial. The effective work has started in October, 2010. After positive evaluation by 6 referees, the second phase of the DK started at the beginning of 2015. After the successful second prolongation, the third phase has begun in 2019. The preparations, including an almost 300 pages' report+application book, my own 45 minutes' presentation at the forthcoming "Hearing" in October, etc., had caused an enormous amount of work during 12 months prior to October, 2018.
See www.math.tugraz.at/discrete for more details on the DK.

A few "associated" PhD positions may still be available before autumn, 2020.

Journal editors who want me to REFEREE some paper, please first go to Refereeing below and read the inital text.

"Passage forbidden for quadrupeds with riding saddle or packsaddle"

The first of these two pictures was taken at the conference
"Geometric Group Theory, Random Walks, and Harmonic Analysis"
in Cortona (Italy), 13-19 June 2004.
You can have a look at the picture gallery of that conference.

The second picture was taken 10 years later, at a different entrance into the town of Cortona, at the conference
"Groups, Graphs, and Random Walks"
2-6 June 2014.
You can also have a look at the picture gallery of this more recent conference.

About myself

I was born in Vienna in 1954. I studied Mathematics at Vienna University of Technology (MSc - "Diplomingenieur") and the University of Salzburg (PhD).

For 6 years (1982-88) I was Assistant Professor ("Universitätsassistent") at the Institut für Mathematik und Angewandte Geometrie of the Montanuniversität Leoben in Austria.

In 1984/85, I was on leave for a year at the Dipartimento di Matematica "G. Castelnuovo" of the University of Rome_I.

A few years later, in 1988, I moved to Italy permanently. For 6 years (1988-94) I was associate professor at the Dipartimento di Matematica "F. Enriques" of the University of Milan, then for 4 years full professor at the same University and, in the last year, at the Dipartimento di Matematica e Applicazioni of the newly founded Universita` di Milano-Bicocca.

I married in 1988, we have one daughter (born in June 1998). In September 1999 we came back to Austria. I am now a full professor in Institut für Diskrete Mathematik (new webpage under construction; formerly Institut für Mathematische Strukturtheorie) of Technische Universität Graz in Austria.

From 2000 to 2003, I served as the Secretary ("Schriftführer") of the Austrian Mathematical Society ÖMG.

My Erdös number is 2, thanks to Carsten Thomassen.

You can look at my mathematical genealogy.

You can also have a look at some pictures that I took during my 50th birthday hike in the Styrian alps, to see how nice Styria is. I also have a small photo gallery of Graz pictures for all those who might want to get an idea how the town looks like, and a photo gallery of pictures from the beautiful wine and castle hills South of Graz.
Regarding more ambitious photography in a somewhat different style, see below, Photography by W.W.

On the last day of my trip to Japan in summer 2007, I prepared a small page on my Japanese travel experiences (including a few pictures).

My 55th birthday hike pictures are from the Tyrolean mountains.

And my 60th birthday hike pictures are from the Monti Sibillini on the border between the Italian regions of Umbria and Marche.

At the conference "Boundaries and Ergodic Geometry", Notre Dame (Indiana) 2015, I took some pictures which can be found here.

My 66th birthday hike pictures are again from Mount Habicht (3277m), where I started (from Gschnitz, 1250m) in the darkness and had the sunrise a bit below the summit. In fact, this was 29 days after the birthday, preceded by other hikes.

Curriculum vitae and List of publications (pdf files).

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Research interests

- Random walks on infinite graphs and groups
- Discrete potential theory
- Boundary theory and harmonic functions
- Structure of infinite graphs, groups and formal languages

Here are two older introductory papers (pdf) to the topic of random walks: One by myself, at a very elementary level and in German (from the book "Zur Kunst des formalen Denkens"), and the other, more advanced, by L. Saloff-Coste (from the Notices of the American Mathematical Society).

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Austrian Science Fund projects

From October 2002 to July 2006, I have run the project entitled "Asymptotic Properties of Random Walks on Graphs" which was funded by the FWF (Austrian Science Fund), project number FWF-P15577-N05. Funding consisted primarily of the salaries for PostDoc or PhD fellows.
You can have a look at the project description and the final report (pdf files). The FWF requires final reviews from the project referees. The - very friendly - project referee has written a very nice final review (pdf file). I only have vague ideas who this referee might be, but in any case would like to express my gratitude here.

From October 2006 to March 2011, I was running a second FWF project entitled "Random walks, random configurations, and horocyclic products", project number FWF-P19115-N18. Here is the (initial) project description (pdf) as well as the final report (pdf) and the project referee's final review (pdf).

From May 2012 to November 2017, I have been running the next FWF project, number FWF-P24028-N18, entitled "Hyperbolic structures in stochastics, graph theory and topology". (The title is in part due to Agelos Georgakopoulos.) Here is the proposal text (pdf) as well as the final report (pdf) and the final review (pdf) of one reviewer.

Link: FWF-P24028-N18: List of project publications

In the meantime, I have obtained a last follow-up project before my retirement scheduled for October, 2022. It title is "Walks and Boundaries - a Wide Range", project number FWF-P31889-N35. It has started in spring, 2019. Here is the proposal text (pdf)

Link: FWF-P31889-N35: List of project publications

Besides these projects, there is the Doctoral College (DK) "Discrete Mathematics" starting in 2010, of which I am the speaker.

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Three books and four proceedings volumes

  1. W. Woess: Denumerable Markov Chains - Generating Functions, Boundary Theory, Random Walks on Trees , EMS Textbooks in Mathematics, European Mathematical Society Publishing House, xviii+351 pages, 2009.
    Book reviews: Mathematical Reviews (pdf), Zentralblatt (pdf). Individual feedback (pdf)
    Once a book is published, as the author one is bound to find some mistake or misprint every time one opens it. After resisting to open it for quite a while, I just (April, 2010) found one such mistake: on page 190, the random time "bold epsilon" is not a stopping time. However, this wrong statement is irrelevant for what follows. Another little misprint was pointed out to my by Irving Glick (May, 2010): on page 16, last line, the sum should start with n=1. As more misprints will come up, I'll probably create a small sub-page with all this.
    Regarding the potential theoretic issues of Section 6, I found it desirable to provide some additional remarks on the Riesz decomposition for superharmonic functions that are not necessarily bounded below (pdf file).

  2. W. Woess: Random Walks on Infinite Graphs and Groups, Cambridge Tracts in Mathematics 138, Cambridge University Press, 334+xi pages, 2000. Paperback re-edition, 2008.
    ERRATA - Four pages of "errata" regarding various misprints and three "true" mistakes. Last updated in January, 2015.
    Book reviews: Mathematical Reviews (pdf), Zentralblatt (pdf), Bull. London Math. Soc. (pdf; attention - text starts on bottom of page); Acta Sci. Math. (Szeged) (pdf), Bulletin Amer. Math. Soc. (pdf), Nieuw Archief voor Wiskunde (pdf).

  3. W. Woess: Catene di Markov e Teoria del Potenziale nel Discreto, Quaderni dell' Unione Matematica Italiana 41, 165+iii pages, 1996.
    Book review: Zentralblatt (pdf).

  4. D. Lenz, F. Sobieczky and W. Woess (editors): Random Walks, Boundaries and Spectra, Proceedings (Graz - St. Kathrein, 2009), Progess in Probability, vol 64. Birkhäuser, Basel, 324+xxvi pages, 2011.

  5. V. A. Kaimanovich with K. Schmidt and W. Woess (editors): Random Walks and Geometry, Proceedings (ESI, Vienna, 2001), de Gruyter, Berlin, 532+x pages, 2004.

  6. P. M. A. Grabner, W. Woess (editors): Fractals in Graz 2001: Analysis - Dynamics - Geometry - Stochastics, Proceedings (Graz 2001), Birkhäuser, Basel, 283+iii pages, 2003.

  7. M. A. Picardello, W. Woess (editors): Random Walks and Discrete Potential Theory, Proceedings (Cortona 1997), Symposia Mathematica XXXIX, Cambridge University Press, 361+ix pages, 1999.

  8. Back to table of contents.

Papers (most of them downloadable)

ATTENTION: for various reasons, download requires insertion of username and password. The Username: author's name. Password: author's birth town = Austria's capital. Initial letters should be uppercase.

All downloads are pdf. The "Remark"s appearing in the list are popups containing some personal background.

  1. T. Hirschler and W. Woess: Laplace and bi-Laplace equations for directed networks and Markov chains, preprint, TU Graz (2020).

  2. E. Sava-Huss and W. Woess: Boundary behaviour of λ-polyharmonic functions on regular trees, Annali di Matematica Pura ed Applicata, online.

  3. M. Peigné and W. Woess: Recurrence of 2-dimensional queueing processes, and random walk exit times from the quadrant, Preprint, Univ. Tours / TU Graz (2019)

  4. Ch. Lindorfer and W. Woess: The language of self-avoiding walks, Combinatorica, online.

  5. T. Hirschler and W. Woess: Polyharmonic functions for finite graphs and Markov chains, to appear in "Frontiers in Analysis and Probability: in the Spirit of the Strasbourg-Zürich Meetings", Springer.

  6. M. A. Picardello and W. Woess: Multiple boundary representations of λ-harmonic functions on trees, London Math. Soc. Lecture Notes 461 (2020) 95-125.

  7. M. A. Picardello and W. Woess: Boundary representations of λ-harmonic and polyharmonic functions on trees, Potential Analysis 51 (2019) 541-561.

  8. J. Kloas and W. Woess: Multidimensional random walk with reflections, Stochastic Proc. Appl. 129 (2019) 336-354.

  9. A. Bendikov, W. Cygan and W. Woess: Oscillating heat kernels on ultrametric spaces, Journal of Spectral Theory 9 (2019) 195–226.

  10. T. Hirschler and W. Woess: Comparing entropy rates on finite and infinite rooted trees with length functions, IEEE Trans. Information Theory 64 (2018) 5570-5580.

  11. A. Bendikov, L. Saloff-Coste, M. Salvatori and W. Woess: Brownian motion on treebolic space: positive harmonic functions, Ann. Institut Fourier (Grenoble) 66 (2016) 1691-1731.

  12. T. Boiko and W. Woess: Moments of Riesz measures on Poincaré disk and homogeneous tree -- a comparative study, Expositiones Math. 33 (2015) 353-374.
    ATTENTION: there is a stupid mistake in formula (2.8), relating the Euclidean with the hyperbolic Laplacian: a square is missing, the factor should be   (1-|z|2)2 / 4

  13. J. Parkinson and W. Woess: Regular sequences and random walks in affine buildings, Ann. Institut Fourier (Grenoble) 65 (2015) 675-707.

  14. A. Bendikov, L. Saloff-Coste, M. Salvatori and W. Woess: Brownian motion on treebolic space: escape to infinity, Revista Matematica Iberoamericana 31 (2015) 935–976.

  15. A. Bendikov, A. Grigor'yan, Ch. Pittet and W. Woess: Isotropic Markov semigroups on ultra-metric spaces, Uspekhi Mat. Nauk 69 (2014) No. 4 (418), 3-102. Link to Russian version. English original in Russian Math. Surveys 69 (2014) No. 4, 589-680. Remark 1 - Remark 2

  16. W. Woess: What is a horocyclic product, and how is it related to lamplighters ?, Internat. Math. Nachrichten of the Austrian Math. Soc. 224 (2013) 1-27. Remark

  17. W. Woess: On the duality between jump processes on ultrametric spaces and random walks on trees, unpublished manuscript (2012). Remark

  18. W. Woess: Context-free pairs of groups. II - Cuts, tree sets, and random walks, Discrete Mathematics 312 (2012) 157-173.

  19. T. Ceccherini-Silberstein and W. Woess: Context-free pairs of groups. I - Context-free pairs and graphs, European J. Combinatorics 33 (2012) 1449-1466.

  20. S. Brofferio, M. Salvatori and W. Woess: Brownian motion and harmonic functions on Sol(p,q), Internat. Math. Research Notes (IMRN) 22 (2012) 5182-5218.

  21. M. Peigné and W. Woess: Stochastic dynamical systems with weak contractivity properties, II. Iteration of Lipschitz mappings, Colloquium Math. 125 (2011) 55-81.

  22. M. Peigné and W. Woess: Stochastic dynamical systems with weak contractivity properties, I. Strong and local contractivity. With a chapter featuring results of Martin Benda, Colloquium Math. 125 (2011) 31-54. Remark

  23. A. Bendikov, L. Saloff-Coste, M. Salvatori and W. Woess: The heat semigroup and Brownian motion on strip complexes, Advances in Mathematics 226 (2011) 992-1055.

  24. W. Huss, E. Sava and W. Woess: Entropy sensitivity of languages defined by infinite automata, via Markov chains with forbidden transitions, Theoretical Computer Science 411 (2010), 3917-3922.

  25. L. Saloff-Coste and W. Woess: Computations of spectral radii on G-spaces, Contemporary Math. 484 (2009) 195-218.

  26. F. Lehner, M. Neuhauser and W. Woess: On the spectrum of lamplighter groups and percolation clusters, Mathematische Annalen 342 (2008) 69-89.

  27. L. Bartholdi, M. Neuhauser and W. Woess: Horocyclic products of trees, J. European Math. Society 10 (2008) 771-816.

  28. D. I. Cartwright and W. Woess: The spectrum of the averaging operator on a network (metric graph), Illinois J. Math. 51 (2007) 805-830.

  29. A. Karlsson and W. Woess: The Poisson boundary of lamplighter random walks on trees, Geometriae Dedicata 124 (2007) 95-107.

  30. R. Ortner and W. Woess: Non-backtracking random walks and cogrowth of graphs, Canadian J. Math.59 (2007) 828-844.

  31. M. Peigné and W. Woess: On recurrence of reflected random walk on the half-line, with an appendix on results of Martin Benda, preprint, TU Graz (2006). Remark

  32. S. Brofferio and W. Woess: Positive harmonic functions for semi-isotropic random walks on trees, lamplighter groups, and DL-graphs, Potential Analysis 24 (2006) 245-265.

  33. L. Saloff-Coste and W. Woess: Transition operators on co-compact G-spaces, Revista Matematica Iberoamericana 22 (2006) 747-799. Remark

  34. S. Brofferio and W. Woess: Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel-Leader graphs, Annales Inst. H. Poincaré (Prob. & Stat.) 41 (2005) 1101-1123, Erratum .

  35. W. Woess: A note on the norms of transition operators on lamplighter graphs and groups, Int. J. Algebra and Computation 15 (2005) 1261-1272.

  36. L. Bartholdi and W. Woess: Spectral computations on lamplighter groups and Diestel-Leader graphs, J. Fourier Analysis Appl. 11 (2005) 175 - 202.

  37. W. Woess: Lamplighters, Diestel-Leader graphs, random walks, and harmonic functions, Combinatorics, Probability & Computing 14 (2005) 415-433.

  38. D. I. Cartwright and W. Woess: Isotropic random walks in a building of type Ad~, Math. Zeitschrift 247 (2004) 101-135.

  39. W. Woess: Generating function techniques for random walks on graphs, in "Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces", P. Auscher, Th. Coulhon and A. Grigor'yan, eds. Contemporary Math. 338 (2003) 391-423.

  40. T. Ceccherini-Silberstein and W. Woess: Growth-sensitivity of context-free languages, Theoretical Comp. Sci. 307 (2003), 103-116. Remark

  41. T. Ceccherini-Silberstein and W. Woess: Growth and ergodicity of context-free languages, Transactions Amer. Math. Soc. 354 (2002) 4597-4625.

  42. T. Nagnibeda and W. Woess: Random walks on trees with finitely many cone types, J. Theoret. Probab. 15 (2002) 399-438. Remark

  43. V. A. Kaimanovich and W. Woess: Boundary and entropy of space homogeneous Markov chains, Ann. Probab. 30 (2002) 323-363.

  44. W. Woess: Heat diffusion on homogeneous trees, Bollettino Un. Mat. It. 4-B (2001) 703-709 and Erratum (caused by printer), Bollettino Un. Mat. It. 5-B (2002) 259-260. Remark

  45. S. Brofferio and W. Woess: On transience of card shuffling, Proc. Amer. Math. Soc. 129 (2001) 1513-1519.

  46. N. Seifter and W. Woess: Approximating graphs with polynomial growth, Glasgow Math. J. 42 (2000) 1-8.

  47. W. Woess: A note on tilings and strong isoperimetric inequality, Math. Proc. Cambridge Phil. Soc. 124 (1998) 385-393. Remark

  48. L. Saloff-Coste and W. Woess: Transition operators, groups, norms, and spectral radii, Pacific J. Math. 180 (1997) 333-367.

  49. P. J. Grabner and W. Woess: Functional iterations and periodic oscillations for random walk on the Sierpinski graph, Stochastic Proc. Appl. 69 (1997) 127-138.

  50. L. Saloff-Coste and W. Woess: Computing norms of group-invariant transition operators, Combinatorics, Probability, and Computing 5 (1996) 161-178.

  51. W. Woess: Dirichlet problem at infinity for harmonic functions on graphs, International Conference on Potential Theory 1994, Proceedings (editors: J. Kral et al.), de Gruyter, Berlin (1996) 189-217.

  52. V. A. Kaimanovich and W. Woess: Construction of discrete, non-unimodular hypergroups, in: "Probability Measures on Groups and Related Structures", Proceedings, Oberwolfach 1994 (editor: H. Heyer), World Scientific, Singapore (1995) 196--209. (No download available.)

  53. W. Woess: The Martin boundary for harmonic functions on groups of automorphisms of a homogeneous tree, Monatshefte für Mathematik 120 (1995) 55-72.

  54. W. Woess: Topological groups and recurrence of quasi transitive graphs, Rendiconti Sem. Mat. Fis. Milano (1994) 185-213.

  55. M. A. Picardello and W. Woess: The full Martin boundary of the bi-tree, Ann. Probab. 22 (1994) 2203-2222.

  56. D. I. Cartwright, V. A. Kaimanovich and W. Woess: Random walks on the affine group of local fields and of homogeneous trees, Ann. Institut Fourier (Grenoble) 44 (1994) 1243-1288.

  57. W. Woess: Random walks on infinite graphs and groups - a survey on selected topics, Bull. London Math. Soc. 26 (1994) 1-60. Remark

  58. S. Giulini and W. Woess: The Martin boundary of the Cartesian product of two hyperbolic spaces, J. Reine Angew. Math. 444 (1993) 17-28.

  59. W. Woess: Fixed sets and free subgroups of groups acting on metric spaces, Math. Zeitschrift 214 (1993) 425-440. Remark

  60. C. Thomassen and W. Woess: Vertex-transitive graphs and accessibility, J. Combinatorial Th., Ser. B. 58 (1993) 248-268.

  61. D. I. Cartwright, P. M. Soardi and W. Woess: Martin and end compactifications for nonlocally finite graphs, Transactions Amer. Math. Soc. 338 (1993) 679-693.

  62. W. Imrich, N. Sauer and W. Woess: The average size of nonsingular sets in a graph, in: "Finite and Infinite Combinatorics in Sets and Logic", editor: N. Sauer et al., Kluwer, Dordrecht (1993), 199-205.

  63. M. A. Picardello and W. Woess: Martin boundaries of Cartesian products of Markov chains, Nagoya Math. J. 128 (1992) 153-169.

  64. V.A. Kaimanovich and W. Woess: Behaviour at infinity and Dirichlet problem for random walks on graphs with a strong isoperimetric inequality, Probability Theory Rel. Fields. 91 (1992) 445-466.

  65. M. A. Picardello, M. H. Taibleson and W. Woess: Harmonic measure of the planar Cantor set from the viewpoint of graph theory, Discrete Math. 109 (1992) 193-202.

  66. D. I. Cartwright and W. Woess: Infinite graphs with nonconstant Dirichlet finite harmonic functions, SIAM J. Discrete Math. 5 (1992) 380-385.

  67. W. Woess: Behaviour at infinity and harmonic functions of random walks on graphs, in "Probability Measures on Groups, X" (H. Heyer, editor), Proceedings, Oberwolfach (1990), Plenum Press, New York (1991) 437-458. (no download available)

  68. M. A. Picardello and W. Woess: Examples of stable Martin boundaries of Markov chains, in "Potential Theory", (M. Kishi, editor), Proceedings, Nagoya 1990, de Gruyter, Berlin (1991) 262-270.

  69. M. A. Picardello, M. H. Taibleson and W. Woess: Harmonic functions on Cartesian products of trees with finite graphs, J. Functional Analysis 102 (1991) 379-400.

  70. P. M. Soardi and W. Woess: Uniqueness of currents in infinite resistive networks, Discrete Applied Math. 31 (1991) 37-49.

  71. W. Woess: Topological groups and infinite graphs, Discrete Math. 95 (1991) 373-384. Remark

  72. P. M. Soardi and W. Woess: Amenability, unimodularity, and the spectral radius of random walks on infinite graphs, Math. Zeitschrift 205 (1990) 471-486.

  73. M. A. Picardello and W. Woess: Ends of infinite graphs, potential theory, and electrical networks, in "Cycles and Rays: Basic Structures in Finite and Infinite Graphs", NATO ASI Series, Montréal. editor: G. Hahn, G. Sabidussi, R. E. Woodrow. Kluwer, Dordrecht (1990) 181-196.

  74. W. Woess: Boundaries of random walks on graphs and groups with infinitely many ends, Israel J. Math. 68 (1989) 271-301.

  75. W. Woess: Amenable group actions on infinite graphs, Math. Annalen. 284 (1989) 251-265.

  76. C. D. Godsil, W. Imrich, N. Seifter, M. E. Watkins and W. Woess: On bounded automorphisms of infinite graphs, Graphs and Combinatorics 5 (1989) 333-338.

  77. B. Mohar and W. Woess: A survey on spectra of infinite graphs, Bull. London Math. Soc. 21 (1989) 209-234.

  78. M. A. Picardello and W. Woess: A converse to the mean value property on homogenous trees, Transactions Amer. Math. Soc. 311 (1989) 209-225.

  79. W. Woess: Graphs and groups with tree-like properties, J. Combinatorial Th., Ser. B, 47 (1989) 361-371. Remark

  80. M. A. Picardello and W. Woess: Harmonic functions and ends of graphs, Proc. Edinburgh Math. Soc. 31 (1988) 457-461.

  81. M. A. Picardello and W. Woess: Finite truncations of random walks on trees (appendix to: A. Korànyi, M. A. Picardello, M. Taibleson: Hardy-spaces on non-homogeneous trees), Symposia Math. 29 (1988) 255-265. (no download available)

  82. W. Woess: Random walks on infinite graphs, in: "Stochastics in Combinatorial Optimization", CISM Lecture Notes, Udine. editor: G. Andreatta, F. Mason, P. Serafini. World Scientific, Singapore (1987) 255-263. (no download available)

  83. W. Woess: Context-free languages and random walks on groups, Discrete Math. 67 (1987) 81-87.

  84. M. A. Picardello and W. Woess: Martin boundaries of random walks: ends of trees and groups, Transactions Amer. Math. Soc. 302 (1987) 185-205.

  85. W. Woess: Harmonic functions on infinite graphs, Rendiconti Sem. Mat. Fis. Milano 56 (1986) 51-63.

  86. W. Woess: A description of the Martin boundary for nearest neighbour random walks on free products, in "Probability Measures on Groups VIII" (editor: H. Heyer), Lecture Notes in Math. 1210(1986) 203-215.

  87. W. Woess: Nearest neighbour random walks on free products of discrete groups, Bollettino Unione Mat. Italiana 5-B (1986) 691-982. Remark

  88. W. Woess: Transience and volumes of trees, Archiv. d. Math. 46 (1986) 184-192.

  89. W. Woess: A short computation of the norms of free convolution operators, Proc. Amer. Math. Soc. 96 (1986) 167-170. Remark

  90. P. Gerl and W. Woess: Local limits and harmonic functions for nonisotropic random walks on free groups, Probability Theory Rel. Fields 71 (1986) 341-355.

  91. P. Gerl and W. Woess: Simple random walks on trees, European J. Combinatorics 7 (1986) 321-331. (no download available)

  92. M. A. Picardello and W. Woess: Random walks on amalgams, Monatshefte für Mathematik 100 (1985) 21-33.

  93. W. Woess: Random walks and periodic continued fractions, Advances in Applied Probability 17 (1985) 67-84.

  94. W. Woess: Chaotic random walks on certain abelian groups, Colloquia Math. Soc. Janos Bolyai 36 (1985) 1147-1167. (no download available)

  95. W. Woess: Harmonic functions on free groups, in "Probabilités sur les Structures Géometriques", editor: G. Letac. Proceedings, Toulouse (1984) 141-153. (no download available)

  96. W. Woess: A random walk on free products of finite groups, in "Probability Measures on Groups", Oberwolfach 1983, editor: H. Heyer. Springer Lect. Notes in Math. 1064 (1984) 467-470. (no download available)

  97. W. Woess: Cogrowth of groups and simple random walks, Archiv d. Math. 41 (1983) 363-370. Remark

  98. W. Woess: Puissances de convolution sur les groupes libres ayant un nombre quelconque de générateurs, Inst. Elie Cartan 7 (1983) 181-190. (no download available) Remark

  99. W. Woess: Périodicité de mesures de probabilité sur les groupes topologiques, Inst. Elie Cartan 7 (1983) 170-180. (no download available) Remark

  100. W. Woess: A local limit theorem for random walks on certain discrete groups, in "Probability Measures on Groups" (editor: H. Heyer), Lecture Notes in Math. 928 (1982) 467-477. Remark

  101. W. Woess: Aperiodische Wahrscheinlickeitsmaße auf topologischen Gruppen, Monatshefte für Mathematik 90 (1980) 339-345.

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Since 1997, I have been the (co-)organizer of several conferences about random walks and related subjects.

Random Walks and Discrete Potential Theory

This conference took place in the week June 22 - June 28, 1997. It was organized by Vadim A. Kaimanovich, Massimo Picardello, Laurent Saloff-Coste and myself. You can have a look at the ps-file containing program and list of participants. The proceedings volume Random Walks and Discrete Potential Theory was edited by Massimo Picardello and myself.

2001 - Random Walks in Vienna

In the period February - July 2001, Vadim Kaimanovich (Rennes), Klaus Schmidt (Vienna) and myself have organized special semester on RANDOM WALKS at the Erwin Schrödinger Institute in Vienna. Deatils of the program can be found here.

Fractals in Graz 2001

In the week June 4--9, 2001, there was a conference with this title (subtitle: Analysis - Dynamics - Geometry - Stochastics) at the Technical University of Graz, as a complement to the ESI programme on Random Walks. The organizing committee consisted of Martin Barlow (Vancouver), Robert Strichartz (Ithaca), Peter Grabner (Graz) and myself. For further informations, see http://finanz.math.tu-graz.ac.at/~fractal/.

Cortona conference in 2004

In the week 13-19 June 2004, there was a conference on "Geometric Group Theory, Random Walks, and Harmonic Analysis" in Cortona (Italy). For more information (pictures !), click on the conference title.

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Special session in Mainz, 2005

In the days 16-19 June 2005, there was a Joint meeting of AMS, DMV and ÖMG at Mainz, Germany. (ÖMG=Austrian Math. Soc.) Within that meeting, a joint session on Stochastic Analysis on Metric Spaces was organized by Laurent Saloff-Coste (Cornell Univ.), Karl-Theodor Sturm (Univ. Bonn) and myself. Main speakers at the special session were B. Driver (UC San Diego), F. Götze (Univ. Bielefeld), G. Lawler (Cornell Univ.) and K.-Th. Sturm (Univ. Bonn).

ESI workshop in spring 2006

In the two weeks March 12-25 March 2006, there was an RDSES/ESI Educational Workshop on Discrete Probability at the Erwin Schrödinger Institute (ESI) in Vienna. Organzers: V.A. Kaimanovich (Bremen), K. Schmidt (Vienna) and myself. Among other, there were be 4 minicourses, held by P. Diaconis, A. Gamburd, G. Lawler, and Ch. Pittet.

Workshop on "Boundaries"
June 29 - July 4, 2009, TU Graz

within the EU Curie program "GROUPS: European training courses and conferences in group theory".

Conference webpage

Scientific committee: Tatiana Nagnibeda, Christophe Pittet, Hamish Short, Wolfgang Woess

Local committee: Ecaterina Sava, Wilfried Huss, Wolfgang Woess

List of selected speakers and participants: Alexander BENDIKOV, Philippe BOUGEROL, Emmanuel BREUILLARD, Donald CARTWRIGHT, Manfred DENKER, Ewa DAMEK, Martin DUNWOODY, Anna ERSCHLER, Vadim KAIMANOVICH, Francois LEDRAPPIER, Volodimyr NEKRASHEVICH, Panos PAPAZOGLOU, James PARKINSON, Massimo PICARDELLO, Tim RILEY, Klaus SCHMIDT, Tim STEGER, Anton THALMAIER, Anatoly VERSHIK

While scientifically successful, the administrative part of this was an absolute nightmare. The money did not arrive in time, and the EU rules which we had to implement were extremely complicated and even contradictory, almost impossible to comply with. In spite of the fact that I tried to prepare it very carefully, a deficit of 1100-1300 Euro was left behind. Reasons were twofold: (1) nobody did tell me at the beginning that I can only declare costs diminuished by VAT, so we had to pay VAT on hotel bills etc., but won't get it back; (2) since the money for the workshop had not arrived in time, it was suggested to me to ask for interim funding from my university, but nobody told me then that the university takes away interests for this loan. Almost all EU projects come along with an overhead from which one can pay such amounts, except for this type of activity (European conferences and training courses).
The whole story has been turning me from an "EU-Paulus" into an "EU-Saulus". Apparently, EU burocracy is like an alien that we are unaware of, breeding in our stomach. When the stomach explodes and the alien emerges, it is not the slimy monster of the movies, but has the appearance of a clerk from some Kafka novel. (Well, I'm still a strong supporter of EU as a union beyond just economic issues - but not as a buerocratic monster!)

Workshop "Analytic enumeration methods in combinatorics, probability and number theory"
May 27 - 28, 2010, TU Graz

Workshop webpage

Local & scientific committee: Ecaterina Sava, Wilfried Huss, Wolfgang Woess
Main speakers: Jozef BECK, Michael DRMOTA, Steve LALLEY, Stephan WAGNER

Spring school "Discrete probability, ergodic theory and combinatorics"
April 4-15, 2011, TU Graz

Workshop webpage

Courses by Geoffrey GRIMMETT, Jeff STEIF, Anders KARLSSON, Michael BJÖRKLUND"
Local & scientific committee: Ecaterina Sava, Wolfgang Woess
Funding by FWF, TU Graz, ESF, ÖMG

Focussed meeting: "the shape of branching random walk and related topics"
July 9-11, 2012, TU Graz


Talks by Steve Lalley (Chicago), Francois Ledrappier (Paris) and others.
Local & scientific committee: Ecaterina Sava, Wolfgang Woess
Funding by FWF, TU Graz, ESF

Leoben-Ljubljana Graph Theory seminar 2013
September 15-18th, Bildungshaus Mariatrost, Graz

Unfortunately, the seminar webpage is no more available.

Keynote speakers: Myhyun KANG (Graz), Jan KRATOCHWIL (Prague)
Local & scientific committee: Wilfried Huss, Norbert Seifter, Wolfgang Woess
Funding by FWF, TU Graz, MU Leoben, ÖMG

Austrian Stochastic Days 2016
June 30 + July 1, 2016, TU Graz


Invited talks by Mathias Beiglböck (Vienna) and Rudolf Grübel (Hannover).
Local & scientific committee: Ecaterina Sava-Huss, Wolfgang Woess
Funding by TU Graz

Leoben-Ljubljana Graph Theory seminar 2016
September 25-28, 2016, JUFA Judenburg

Seminar webpage

Keynote speakers: Chris GODSIL (Waterloo), Aleksander MALNIC (Lljubljana), Rögnvaldur Möller (Reykjavik), Vladimir TROFIMOV (Jekaterinburg),
Local & scientific committee: N.N., Wolfgang Woess
Funding by FWF, ÖMG, MU Leoben, town of Judenburg

Groups, Probability, Dynamics

A meeting on the occasion of the 50th birthday of Tullio Ceccherini-Silberstein
February 22-24, 2017, Rome


Invited speakers: Alexander Bufetov (Moscow / Marseille), Michel Coornaert (Strasbourg), Rostislav Grigorchuk (College Station), Vadim Kaimanovich (Ottawa), Tatiana Nagnibeda (Geneva), Klaus Schmidt (Vienna), Stanislav Smirnov (Geneva), Alain Valette (Neuchatel)

Organising committee: Daniele D'Angeli, Alfredo Donno, Fabio Scarabotti, Filippo Tolli, Wolfgang Woess
Funding by: Dipartimento S.B.A.I. - Sapienza Università di Roma
Dipartimento di Matematica e Fisica - Università Roma Tre

Geometric Analysis and Potential Theory
- Discrete and Continuous

A meeting on the occasion of the 70th birthday of Massimo A. PICARDELLO
February 17-19, 2020, Perugia


Invited speakers: Nicola Arcozzi (Univ. Bologna, Italy), Marek Bozejko (Wroclaw University, Poland), Joel M Cohen (University of Maryland, USA), Flavia Colonna (George Mason University, USA), Jacques Faraut (Université Pierre et Marie Curie - Paris 6, France), Simon G. Gindikin (Rutgers University, USA), Alessandra Iozzi (ETH Zürich, Switzerland), Vadim A Kaimanovich (Univ. Ottawa, Canada), Gabriella Kuhn (Università di Milano - Bicocca, Italy), Beatrice Pelloni (Heriott Watt Univ., Scotland), Florin Radulescu (Università di Roma - Tor Vergata, Italy), Fulvio Ricci (Scuola Normale Superiore di Pisa, Italy), Peter Sjögren (University of Gothenburg, Sweden)

Organising committee: Enrico Casadio-Tarabusi, Fausto DiBiase, Mauo Pagliacci, Wolfgang Woess

Groups, Random Walks and Dynamics

A conference on the occasion of the 60th birthday of Vadim A. KAIMANOVICH
June 15-18, 2020, Paris


Invited speakers: Laurent Bartholdi, Itai Benjamini, Jérémie Brieussel, Marc Burger, Alex Eskin (to be confirmed), Joshua Frisch, Alex Furman, Agelos Georgakopoulos, Sebastien Gouëzel, Rostislav Grigorchuk, Yair Hartman, Kate Juschenko, Olga Kharlampovich, François Ledrappier, Jean Mairesse, Nicolas Monod, Tatiana Nagnibeda, Volodymir Nekrashevych, Yuval Peres, Laurent Saloff-Coste, Omer Tamuz, Ryokichi Tanaka, Giulio Tiozzo, Anatoly Vershik, Tianyi Zheng

Organising committee: Sami Abbes, Sara Brofferio, Anna Erschler, Wolfgang Woess

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Laurent Bartholdi
Sara Brofferio
Alexander Bendikov
Donald I. Cartwright
Tullio Ceccherini-Silberstein
Wojciech Cygan
Peter Gerl
Saverio Giulini
Peter J. Grabner
Chris D. Godsil
Alexander Grigor'yan
Wilfried Huss
Thomas Hirschler
Wilfried Imrich
Vadim A. Kaimanovich
Anders Karlsson
Franz Lehner
Judith Kloas
Bojan Mohar
Tatiana Nagnibeda
Markus Neuhauser
Ronald Ortner
James Parkinson
Marc Peigné
Massimo A. Picardello
Christophe Pittet
Laurent Saloff-Coste
Maura Salvatori
Norbert Sauer
Ecaternia Sava
Norbert Seifter
Paolo M. Soardi
Mitch Taibleson
Carsten Thomassen
Mark E. Watkins

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I have acted as the referee for more papers (and some books) than I have published myself.

Important hint for editors who want me to referee a paper: attach the paper to your email!!! Don't try to make me go through some more or less complicated website login procedures before I can even see what I'm supposed to referee. From now on (= November 2014) I will only reply to requests where I can see right away what I'm asked to referee. .....

Throughout the years, I have been a referee for the following journals, resp. conferences or publishers (incomplete list):

Abhandlungen des Mathematischen Seminars der Universität Hamburg;
Advances in Applied Mathematics;
Advances in Mathematics;
Annales Blaise Pascal;
Annales de l'Ecole Normale Superieure;
Annales de l'Institut Fourier (Grenoble);
Annales de l'Institut Poincaré-B;
Annali di Matematica Pura ed Applicata;
Annals of Probability;
Annals of Mathematics;
Archiv der Mathematik;
Bollettino dell'Unione Matematica Italiana;
Bulletin de Sciences Math\'ematiques;
Bulletin of the London Mathematical Society;
Cambridge University Press;
Circuits, Systems, and Signal Processing;
Combinatorics, Probability, and Computing;
Commentarii Mathematici Helvetici;
Contemporary Mathematics;
Discrete and Computational Geometry;
Discrete Mathematics;
Discussiones Mathematicae;
Electronic Comunications in Probability;
Electronic Journal of Probability;
Glasgow Mathematical Journal;
Illinois Journal of Mathematics;
International Journal of Algebra and Computation;
International Journal of Mathematics and Mathematical Sciences;
International Mathematical Research Notes;
Inventiones Mathematicae;
Israel Journal of Mathematics;
Journal of Algebraic Combinatorics;
Journal of Combinatorial Theory-B;
Journal of Functional Analysis;
Journal of Graph Theory;
Journal of Group Theory;
Journal of Lie Theory;
Journal of Mathematical Analysis and Applications;
Journal of Statistical Physics;
Journal of the European Mathematical Society;
Journal of the American Mathematical Society;
Journal of the London Mathematical Society;
Journal of Theoretical Probability;
Linear and Multilinear Algebra;
Mathematische Annalen;
Mathematische Nachrichten;
Mathematische Zeitschrift;
Monatshefte für Mathematik;
Nagoya Mathematical Journal;
Pacific Journal of Mathematics;
Potential Analysis;
Probability Theory and Related Fields;
Proceedings of the London Mathematical Society;
Random Structures and Algorithms;
Springer Lecture Notes in Mathematics;
Transactions of the American Mathematical Society.

From 1990 to 1999 I have served as an Associate Editor of the journal ``Circuits, Systems and Signal Processing'' (Birkhäuser).

In 2007, I have acted as a referee in the evaluation of the Mathematical Insitute of the Slovak Academy of Sciences.

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Please see the relative informations on TUG online.

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On politics

In February 2000, Austria's (at the time) new government, a right wing coalition between Christian Democrats and the (so-called) Freedom Party had led the country into a tempest of national and international criticism and worldwide isolation. This had a particular impact on the scientific comunity, whose work is based on international exchange and cultural openmindendness. This is why, after those events, I had included my personal considerations on Austrian politics in my scientific homepage.

The original text (in particular the one regarding the so-called "sanctions") is now really out of date, so I removed it at last. As a matter of fact, while probably most Austrian colleagues considered this a peculiar thing to put on my webpage, I had quite a bit of positive feedback from abroad.

Subsequently, Austria has disappeared from most international news, and there have been only few news flashes reporting that after only two and a half years, and a full year before the end of its term, the government had collapsed in autumn 2002 because of a major crisis within the Freedom Party. Since 2003, the same coalition was back to power again, but with the Freedom Party down to 10% instead of the previous 27%. Since 2006, after the Freedom Party has disassembled in two pieces, they had been no more represented in the government, and we were back to the "big coalition" between Social and Christian Democrats, even though these two parties appear to hate each other profoundly.

However, in the meantime, the Freedom Party under its new leader has gained votes, and contrary to 2000, it is nowadays "normal" that the right wing is successful on the basis of agressive populism in most democratic countries. Since 2017, we have again the coalition between the Chrsitian Democrats and the Freedom Party. People seem to be happy: the coalition partners do not quarrel. My conclusion is a pessimistic view on the "wisdom" of the sovereign, i.e., the voter: no matter whether there is corruption, illiberal democracy and so on - if the surface appears quiet and peaceful then the majority is happy. They are just happy not to hear about all those things which in a critcal and free environment would become visible.

I repeat: I'm not at all convinced that I'll be able to conclude my days without witnessing some new political repressions, of course with different appearance than in the 1930s and 40s. October 2019: the degree of evilness of the following personalities is of course quite variable.

past: Mussolini - Dollfuss - Hitler - Stalin
recent past: Berlusconi - Haider - LePen (father)
present: Putin - Orban - Kaczynski(Sydlo) - Erdogan - Trump
- Bolsonaro - KicklVilimskyStrache - Salvini - LePen (daughter)

The list comprises persons who (1) came or may come to power through a more or less democratic procedure (this is why Franco, Salazar, Pinochet are not in the list), and (2) are more or less close to our cultural (hemi)sphere (this is why many others, like e.g. Mugabe, Duarte, Maduro are not comprised).

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True stories

This was the title of an almost forgotten movie by "Talking Head" David Byrne. I also have some true stories to tell, regarding Kafkaesque adventures with bucrocracies and politics in different countries, notably Italy and Austria.

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Friedrich Woess (1915-1995)
Elisabeth Woess (1917-2001)

My father, Friedrich Woess, was Professor at Universität für Bodenkultur, Vienna.
He was also gifted in painting (mostly water color). He left about 850 pictures, 99% are landscapes.
I have organized a show of some of them in Summer, 2002.
There was another show in Summer, 2006 (originally planned for 2005).
You can have a look at some of his paintings: those from the exhibition in 2006, and others: part1, part2, part3, part4, all four from two booklets with reproductions from the 1990ies, and Greece 1979.
You can read an accompanying text (in German), and find the announcement of the abovementioned first exhibition in 2002.

My mother, Elisabeth Woess (1917-2001) was also a university professor, at the Institute of Botanics of Vienna University. You can see a few late photographs of her and read an obituary (pdf, in German) that appeared in Verh. Zool.-Bot. Ges. Österreich 138 (2001) 275-278. A posthumuous publication has appeared in Plant Systematics and Evolution 258 (2006) 27-37. It has a small background story: my mother had continued her research work until a week before she passed a way at the age of 84. This was supposed to become a joint work with a Professor in Florida of Hungarian origin who years before had sent her specimen of an antarctic algae to be studied and classified. In the last year of her life she often expressed sadness about the fact that she had finished her part of this work, but her colleague would not complete it. (Indeed, he had retired, too, and had no more laboratory access.) I found the manuscript and drawings in the material that she left behind, and managed to convince the director of the Botanical Insitute in Vienna to take care of its publication. It was carefully revised and re-edited. See in particular the Comments and Acknowledgements at the end of the paper.

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Photography by Wolfgang Woess

Starting with 1979, I became active in the world of auteur photography (Autorenfotografie), thanks to the photographer Kurt Kaindl from Salzburg. Through him, I also got involved in the foundation of the gallery Fotohof in Salzburg. Until 1984, I produced several series of black-and-white photographs; after that I turned mainly to colour (the latter without printing myself). In the 1980ies I had a good number of exhibitions in different locations. After several dissappointments in the photography scene, an since I had moved to the University of Milan in 1988, I have been active with varying commitment and only privately.
I have now started to create a separate page with my work in this type of photography: Fotoseite Wolfgang Woess.

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Link new homepage of the Institute of Discrete Mathematics (still under construction).
Link to the old homepage of Institut für Mathematik C.

Last modified on September 14, 2020.

Für den Inhalt verantwortlich: Wolfgang Woess
Institut für Diskrete Mathematik
TU Graz, Steyrergasse 30, A-8010 Graz