Wolfgang Woess - publications

Wolfgang Woess - publications

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, in April 2010 I 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. Eleven years later: page 143, line 6 from bottom: "= y" instead of "= x". Page 144, line 4: it should be "produces k children". Page 149, in the proof of Theorem 5.54: it should be u(m) = 11...12, not 00...01.
    In April 2023, Jun Kigami pointed out a mistake in the proof of Proposition 1.43. A corrected version can be found here (pdf).
    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).

    You can find a CORRECTED VERSION (2022) here!

  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.

Papers

Most of them are 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. W. Woess: Notes on hyperbolic branching Brwonian motion, work in progress, posted here on April 9, 2024. Remark

  2. M. Salvatori, M. A. Picardello, W. Woess: Polyharmonic potential theory on the Poincaré disk, Journal of Functional Analysis 286, Issue 9 (2024) article no. 110362.

  3. R. I. Möller, W. Woess: Amalgamated products of G-spaces, unfinished manuscript, TU Graz (2020/22). Remark

  4. W. Woess: Some old and basic facts about random walks on groups, arXiv:2209.00319 (2022). Remark

  5. V. A. Kaimanovich and W. Woess: Limit distributions of branching Markov chains, Annales Inst. H. Poincaré - Prob. & Stat. 59, No 4 (2023) 1951-1983.

  6. A. Muranova and W. Woess: Networks with complex weights: Green function and power series, mdpi Mathematics 2022, 10, 820, 20pp.

  7. W. Woess: Ratio limits and Martin boundary, Documenta Math. 26 (2021) 1501-1528.

  8. T. Hirschler and W. Woess: Laplace and bi-Laplace equations for directed networks and Markov chains, Expositiones Mathematicae 39 (2021) 271-301.

  9. E. Sava-Huss and W. Woess: Boundary behaviour of λ-polyharmonic functions on regular trees, Annali di Matematica Pura ed Applicata 200 (2021) 35-50. Remark

  10. M. Peigné and W. Woess: Recurrence of 2-dimensional queueing processes, and random walk exit times from the quadrant, Annals of Applied Probability 31 (2021) 2519-2537.

  11. Ch. Lindorfer and W. Woess: The language of self-avoiding walks, Combinatorica 40 (2020) 691-720.

  12. T. Hirschler and W. Woess: Polyharmonic functions for finite graphs and Markov chains, in "Frontiers in Analysis and Probability: in the Spirit of the Strasbourg-Zürich Meetings", pp. 77-90, Springer (2020).

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

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

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

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

  17. 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.

  18. 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.

  19. 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

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

  21. 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.

  22. 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

  23. 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

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

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

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

  27. 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.

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

  29. 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

  30. 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.

  31. 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.

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

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

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

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

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

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

  38. M. Peigné and W. Woess: On recurrence of reflected random walk on the half-line, with an appendix on results of Martin Benda, arXiv:math/0612306 (2006). Remark

  39. 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.

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

  41. 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 .

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

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

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

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

  46. 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.

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

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

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

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

  51. 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 1, Remark 2

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

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

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

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

  56. 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.

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

  58. 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.

  59. 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. Remark

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

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

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

  63. 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.

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

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

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

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

  68. 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.

  69. 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.

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

  71. 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.

  72. 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.

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

  74. 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.

  75. 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.

  76. 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.

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

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

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

  80. 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.

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

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

  83. 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.

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

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

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

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

  88. 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)

  89. 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)

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

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

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

  93. 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.

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

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

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

  97. 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.

  98. P. Gerl and W. Woess: Simple random walks on trees, European J. Combinatorics 7 (1986) 321-331.

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

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

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

  102. W. Woess: Harmonic functions on free groups, in "Probabilités sur les Structures Géometriques", editor: G. Letac. Proceedings, Toulouse (1985) 141-153.

  103. 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.

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

  105. 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

  106. W. Woess: Périodicité de mesures de probabilité sur les groupes topologiques, Inst. Elie Cartan 7 (1983) 170-180. Remark

  107. 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

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

  109. W. Woess: r-rekurrente Wahrscheinlichkeitsmaße auf topologischen Gruppen, unpublished manuscript (1980). Remark



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Last modified on April 9, 2024.

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