# Robert F. Tichy's Homepage

 Kyoto 2010 After 5 days in the mountains (2008)

List of current courses and lectures
Office: +43/316/873/7120
Fax: +43/316/873/7126
email: tichy@tugraz.at

Institut für Analysis und Computational Number Theory
Technische Universität Graz
Steyrergasse 30
A-8010 Graz
Austria

### Research Interests

Uniform Distribution and Discrepancy
Diophantine Equations
Analytic Combinatorics
Algorithmic Number Theory
Fractal Structures
Asymptotic and Stochastic Analysis
Information Based Complexity
Quasi-Monte Carlo Methods
Mathematics in Finance and Insurance

Head of the Department of Mathematics (TU Graz, 1994-2000)
Co-Speaker of the research area "Number-Theoretic Algorithms and their Applications" (funded by FWF) (2000-2005)
Member of the Senate of the TU Graz (1998-2006)
Member of the Convent of the TU Graz (2003-2004)
Vice-President of the Austrian Mathematical Society (OeMG) (2002-2005)
President of the Austrian Mathematical Society (OeMG) (2006-2009)
Dean (Faculty of Science, TU Graz, 2003), Dean (2004-2009) and Vice-Dean (2010- ) of the Faculty of Mathematical and Physical Sciences
Member of the Board (Kuratorium) of the FWF (Austrian Science Foundation) (2006- )

### Editorial Duties

Journal of Number Theory (1991 - 2000)
Journal de Théorie des Nombres, Bordeaux
Mathematica Slovaca
Fibonacci Quarterly
Grazer Mathematische Berichte
"Number Theoretic Analysis", Lecture Notes in Mathematics volume 1452, Springer 1990, with E. Hlawka
"Algebraic Number Theory and Diophantine Analysis", de Gruyter Proceedings in Mathematics, de Gruyter 2000, with F. Halter-Koch
Integers, Electronic Journal of Combinatorial Number Theory (Member of the Editorial Board, 2006- )
"Diophantine Approximation: Festschrift for Wolfgang Schmidt", Springer 2008, with H.P. Schlickewei and K. Schmidt
"Dependence in Probability, Analysis and Number Theory" (In Memory of Walter Philipp), Kendrick Press 2010, with I. Berkes, R.C. Bradley, H Dehling and M. Peligrad
International Mathematical News (IMN, Austrian Mathematical Society), 2010-

### Professional Positions and Awards

Ph.D. University of Vienna (1979)
Life-Insurance consultant (1979-1981)
Assistant (Vienna, 1980-1983)
Lecturer of Actuarial Sciences (Linz, 1980)
Award of the Austrian Mathematical Society (1985)
Dozent (Habilitation TU Vienna, 1983-1990)
Full Professor (TU Graz, since 1990)
Visiting Positions: Salzburg (1986), Tata Institute Bombay (1992), Marseille (1993, 1995, 2010, 2011), Debrecen (1997), University of Illinois (Urbana-Champaign, 2000), University of the Witwatersrand (Johannesburg, 2003), University of Vienna (2010), Macquarie University Sydney (2010)
Member of the New York Academy of Sciences (1997-2002)
Corresponding Member of the Austrian Academy of Sciences (2004- )
Faculty Member of the doctoral school DK Discrete Mathematics (2010-)
Appointment to the ESF Standing Committee for Physical and Engineering Sciences (PESC, 2011-12)
Austrian delegate in the General Assembly of ICM 2014 in Korea

### Selected Publications

Peter Grabner, Peter Kirschenhofer and Robert Tichy: Combinatorial and arithmetical properties of linear numeration systems. Combinatorica, 22 (2002), 245-267
Hansjörg Albrecher, Jozef Teugels and Robert Tichy: On a gamma series expansion for the time-dependent probability of collective ruin. Insurance / Mathematics & economics, 29 (2001), 345-355
Yuri F. Bilu and Robert Tichy: The diophantine equation f(x)=g(y). Acta arithmetica, 95/3 (2000), 261-288
Michael Drmota and Robert Tichy: Sequences, discrepancies and applications, Springer-Verlag Berlin, 1997
Peter Grabner, Pierre Liardet and Robert Tichy: Odometers and systems of numeration. Acta arithmetica, 70 (1995), 103-123
Philippe Flajolet, Peter Grabner, Peter Kirschenhofer, Helmut Prodinger and Robert Tichy: Mellin transforms and asymptotics: digital sums. Theoretical computer science, 123/2 (1994), 291-314
Peter Grabner and Robert Tichy: alpha-expansions, linear recurrences and the sum-of-digits function. Manuscripta mathematica, 70 (1991), 311-324
Martin Blümlinger, Michael Drmota and Robert Tichy: A uniform law of the iterated logarithm for Brownian motion on compact Riemannian manifolds. Mathematische Zeitschrift, 201/4 (1989), 495-507
Philippe Flajolet, Peter Kirschenhofer and Robert Tichy: Deviations from uniformity in random strings. Probability theory and related fields, 80/1 (1988), 139-150
Robert Tichy: Ein metrischer Satz über vollständig gleichverteilte Folgen. Acta arithmetica, 48/2 (1987), 197-207
Norbert Kopecek, Gerhard Larcher, Robert Tichy and Gerhard Turnwald: On the discrepancy of sequences associated with the sum-of-digits function. Annales de l’Institut Fourier, 37/3 (1987), 1-17
Christian Buchta, Josef S. Müller and Robert Tichy: Stochastical approximation of convex bodies. Mathematische Annalen, 271/2 (1985), 225-235
Harald Niederreiter and Robert Tichy: Solution of a problem of Knuth on complete uniform distribution of sequences. Mathematika, 32/1 (1985), 26-32
Viktor Losert, Werner Georg Nowak and Robert Tichy: On the Asymptotic Distribution of the Powers of $(s\times s)$-Matrices. Compositio mathematica, 45/2 (1982), 273-291
Helmut Prodinger and Robert Tichy: Fibonacci numbers of graphs. The Fibonacci quarterly, 20/1 (1982), 16-21

### Publications since 2000

Markus Hofer, Maria Rita Iaco and Robert Tichy: Ergodic properties of $\beta$-adic Halton sequences. Ergodic theory and dynamical systems, 35 (2015), 895-909
Maria Rita Iaco, Milan Pasteka and Robert Tichy: Measure density for set decompositions and uniform distribution. Rendiconti del Circolo Matematico di Palermo, 64 (2015), 323-339
Maria Rita Iaco, Stefan Michael Thonhauser and Robert Tichy: Distribution functions, extremal limits and optimal transport. Indagationes mathematicae, 26/5 (2015), 823-841
Dijana Kreso and Robert Tichy: Functional composition of polynomials: indecomposability, Diophantine equations and lacunary polynomials. Grazer mathematische Berichte, (2015), 1-24
Manfred Madritsch and Robert Tichy: Dynamical systems and uniform distribution of sequences. arXiv.org [Elektronische Ressource], (2015), to appear
Christoph Aistleitner, Florian Pausinger, Anne Marie Svane and Robert Tichy: On functions of bounded variation. arXiv.org [Elektronische Ressource], (2015), to appear
Bergelson V., Grigori Kolesnik, Manfred Madritsch, Younghwan Son and Robert Tichy: Uniform distribution of prime powers and sets of recurrence and van der Corput sets in Z^k. Israel journal of mathematics, 201 (2014), 729-760
Christopher Frei, Robert Tichy and Volker Ziegler: On sums of s-integers of bounded norm. Monatshefte für Mathematik, 175 (2014), 241-247
István Berkes and Robert Tichy: On permutation-invariance of limit theorems. Journal of complexity, (2014), to appear
Manfred Madritsch and Robert Tichy: Construction of normal numbers via generalized prime power sequences. Journal of integer sequences [Elektronische Ressource], 16 (2013), 17-30
Robert Tichy and István Berkes: Lacunary series and stable distributions. In: Festschrift für Paul Deheuvels, (2013), 135-143
Christoph Aistleitner, István Berkes and Robert Tichy: On permutations of lacunary series. RIMS Kôkyûroku / Bessatsu, B34 (2012), 1-25
Christoph Aistleitner, István Berkes and Robert Tichy: On the law of the iterated logarithm for permuted lacunary sequences. Proceedings of the Steklov Institute of Mathematics = Trudy Matematiceskogo Instituta Imeni V. A. Steklova, 276 (2012), 3-20
Christoph Aistleitner, Markus Hofer and Robert Tichy: A central limit theorem for Latin hypercube sampling with dependence and application to exotic basket option pricing. International journal of theoretical and applied finance, 15 (2012), 1-20
Christoph Aistleitner, István Berkes and Robert Tichy: On the system $f(nx)$ and probabilistic number theory. In: Analytic and Probabilistic Number Theory, n/a (2012), 1-18
Christoph Aistleitner, István Berkes and Robert Tichy: On permutations of Hardy- Littlewood-Pólya sequences. Transactions of the American Mathematical Society, 363 (2011), 6219-6244
Christoph Aistleitner, István Berkes and Robert Tichy: On the asymptotic behavior of weakly lacunary sequences. Proceedings of the American Mathematical Society, 139 (2011), 2505-2517
Fabrizio Barroero, Christopher Frei and Robert Tichy: Additive unit representations in rings over global fields - A survey. Publicationes mathematicae, 79 (2011), 291-307
Robert Tichy and Martin Zeiner: Baire results of multi-sequences. Uniform distribution theory, 5/1 (2010), 13-44
Robert Tichy, Christoph Aistleitner and István Berkes: Lacunary sequences and permutations. In: Dependence in Probability, Analysis and Number Theory, n/a (2010), 35-49
István Berkes, Richard C. Bradley, Herold Dehling, Magda Peligrad and Robert Tichy: Dependence in Probability, Analysis and Number Theory, Kendrick Press Heber City, Utah, USA, 2010
Clemens Josef Fuchs, Robert Tichy and Volker Ziegler: On quantitative aspects of the unit sum number problem. Archiv der Mathematik, 93 (2009), 259-268
Robert Tichy and Johannes Wallner: Johannes Frischauf - eine schillernde Persönlichkeit in Mathematik und Alpinismus. Internationale mathematische Nachrichten = International mathematical news, 210 (2009), 21-32
Robert Tichy: Nachruf auf Edmund Hlawka. Monatshefte für Mathematik, 158 (2009), 107-120
István Berkes, Walter Philipp and Robert Tichy: Entropy conditons for subsequences of random variables with applications to empirical processes. Monatshefte für Mathematik, 153 (2008), 183-204
Volker Ziegler, Robert Tichy and Alan Filipin: The additive unit structure of purely quartic complex fields. Functiones et approximatio, 39 (2008), 113-131
Thomas Stoll and Robert Tichy: Diophantine equations for Morgan-Voyce and other modified orthogonal polynomials. Mathematica Slovaca, 58 (2008), 11-18
Manfred Madritsch, Jörg Thuswaldner and Robert Tichy: Normality of numbers generated by the values of entire functions. Journal of number theory, 128/5 (2008), 1127-1145
István Berkes, Walter Philipp and Robert Tichy: Metric discrepancy results for sequences $\{n_kx\}$ and diophantine equations. In: Diophantine Approximation, 16 (2008), 95-105
Attila Pethö, Clemens Josef Fuchs and Robert Tichy: On the diophantine equation $G_n(x)=G_m(P(x))$ with $Q(x,y)=0$. In: R. Tichy, H.P. Schlickewei, K. Schmidt (eds.): Diophantine Approximation, 16 (2008), 199-209
Robert Tichy and Stephan Wagner: Algorithmic generation of molecular graphs with large Merrifield-Simmons index. Match - communications in mathematical and in computer chemistry, 59 (2008), 239-252
Robert Tichy: Nachruf auf Walter Philipp. Monatshefte für Mathematik, 153 (2008), 177-182
Robert Tichy, Volker Ziegler and Alan Filipin: On the quantitative unit sum number problem - an application of the subspace theorem. Acta arithmetica, 133 (2008), 297-308
Volker Ziegler, Robert Tichy and Stephan Wagner: Graphs, Partitions and Fibonacci Numbers. Discrete applied mathematics, 155/10 (2007), 1175-1187
Volker Ziegler and Robert Tichy: Units generating the ring of integers of complex cubic fields. Colloquium mathematicum, 109/1 (2007), 71-83
Robert Tichy, István Berkes and Walter Philipp: Pseudorandom numbers and entropy conditions. Journal of complexity, 23 (2007), 516-527
István Berkes, Walter Philipp and Robert Tichy: Empirical processes in probabilistic number theory: the LIL for the discrepancy of $(n_kw)$ mod 1. Illinois journal of mathematics, 50 (2006), 107-145
Clemens Heuberger, Attila Pethö and Robert Tichy: Thomas' Family of Thue Equations over Imaginary Quadratic Fields, II. Sitzungsberichte und Anzeiger / Österreichische Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse / 2, 142 (2006), 3-7
Hansjörg Albrecher, Jürgen Hartinger and Robert Tichy: On the distribution of dividend payments and the discounted penalty function in a risk model with linear dividend barrier. Scandinavian actuarial journal, (2005), 103-126
Peter Grabner, Pierre Liardet and Robert Tichy: Spectral Disjointness of Dynamical Systems Related to Some Arithmetic Functions. Publicationes mathematicae, 66 (2005), 213-244
Robert Tichy and Stephan Wagner: Extremal Problems for Topological Indices in Combinatorial Chemistry. Journal of computational biology, 12 (2005), 1004-1013
Jörg Thuswaldner and Robert Tichy: Waring's problem with digital restrictions. Israel journal of mathematics, 149 (2005), 317-344
Ladislav Misik and Robert Tichy: Large null sets in metric spaces. Journal of mathematical analysis and applications, 305 (2005), 424-437
Andrej Dujella, Ivica Gusic and Robert Tichy: On the indecomposability of polynomials. Sitzungsberichte und Anzeiger / Österreichische Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse / 2, 214 (2005), 81-88
Jürgen Hartinger, Reinhold Kainhofer and Robert Tichy: Quasi-Monte Carlo Algorithms for unbounded, weighted integration problems. Journal of complexity, 20/5 (2004), 654-668
Hansjörg Albrecher, Jürgen Hartinger and Robert Tichy: Quasi-Monte Carlo techniques for CAT bond pricing. Monte Carlo methods and applications, 10 (2004), 197-212
Hansjörg Albrecher, Reinhold Kainhofer and Robert Tichy: Simulation Methods in Ruin Models with Non-linear Dividend Barriers. Mathematics and computers in simulation, 62 (2003), 277-287
Hansjörg Albrecher, Jürgen Hartinger and Robert Tichy: Multivariate approximation methods for the pricing of catastrophe-linked bonds. International series of numerical mathematics, 145 (2003), 21-39
Clemens Josef Fuchs and Robert Tichy: Perfect powers in linear recurring sequences. Acta arithmetica, 107/1 (2003), 9-25
Clemens Josef Fuchs, Robert Tichy and Attila Pethö: On the Diophantine equation G_n(x)=G_m(P(x)): higher-order recurrences. Transactions of the American Mathematical Society, 355 (2003), 4657-4681
Gerhard Larcher, Martin Predota and Robert Tichy: Arithmetic average options in the hyperbolic model. Monte Carlo methods and applications, 9 (2003), 227-239
Hansjörg Albrecher, Reinhold Kainhofer and Robert Tichy: Efficient Simulation Techniques for a Generalized Ruin Model. Grazer mathematische Berichte, 245 (2002), 79-110
Reinhold Kainhofer and Robert Tichy: QMC methods for the solution of differential equations with multiple delayed arguments. Grazer mathematische Berichte, 345 (2002), 111-129
Clemens Josef Fuchs, Robert Tichy and Attila Pethö: On the Diophantine equation G_n(x)=G_m(P(x)). Monatshefte für Mathematik, 137/3 (2002), 173-196
Clemens Josef Fuchs, Robert Tichy and Andrej Dujella: Diophantine m-tuples for linear polynomials. Periodica mathematica Hungarica, 45/1-2 (2002), 21-33
Clemens Heuberger, Attila Pethö and Robert Tichy: Thomas' family of Thue equations over imaginary quadratic fields. Journal of symbolic computation, 34 (2002), 437-449
Peter Grabner, Peter Kirschenhofer and Robert Tichy: Combinatorial and arithmetical properties of linear numeration systems. Combinatorica, 22 (2002), 245-267
Hansjörg Albrecher, Jozef Teugels and Robert Tichy: On a gamma series expansion for the time-dependent probability of collective ruin. Insurance / Mathematics & economics, 29 (2001), 345-355
István Berkes, Walter Philipp and Robert Tichy: Pair correlation and U-statistics for independent and weakly dependent random variables. Illinois journal of mathematics, 45 (2001), 559-580
Wolfgang Müller, Jörg Thuswaldner and Robert Tichy: Fractal properties of number systems. Periodica mathematica Hungarica, 42 (2000), 51-68
Hansjörg Albrecher and Robert Tichy: Zur Konvergenz eines Lösungsverfahrens für ein Risikomodell mit gammaverteilten Schäden. Schweizerische Aktuarvereinigung: Mitteilungen, (2000), 115-127
Hansjörg Albrecher, Jiri Matousek and Robert Tichy: Discrepancy of point sequences on fractal sets. Publicationes mathematicae, 56 (2000), 233-249
Yuri F. Bilu and Robert Tichy: The diophantine equation f(x)=g(y). Acta arithmetica, 95/3 (2000), 261-288

You might also like to have a look at some photographs taken at regular mountain tours.
Also, look at some pictures from South Africa (2003)

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