## INFORMATION FOR

# PD Dr. Lorenz Gilch

## Contact

Room: 205 IM

Phone: +49 851 509 3113

Email: lorenz.gilchuni-passau.de

## Scientific Education

11.1997 - 09.2003 Studies of Mathematics at University of Passau with subsidiary subject "Stochastic Methods in Computer Science" and are of specialisation "Applied Statistics"

09.2004 - 03.2007 PhD studies at the Institute of Mathematics C at Graz University of Technology; title of PhD thesis: "Rate of Escape of Random Walks"; supervisor: Prof. Dr. Wolfgang Woess

07.2016 Habilitation in Mathematics at Graz University of Technology; title of habilitation thesis: "Asymptotic Properties of Random Walks via Generating Functions"

## Scientific Career

03.2004 - 08.2008 PhD student and research assistant at the Institute of Mathematics C at Graz University of Technology

09.2008 - 02.2010 DFG (German science fund) grant at the Institute of Mathematics C at Graz University of Technology

03.2010 - 08.2010 Assistant Professor at the Institute of Mathematics C at Graz University of Technology

09.2010 - 02.2011 DFG (German science fund) grant at Section de Mathématiques at Université de Genève/Switzerland

03.2011 - 08.2016 Assistant Professor at the Institute of Mathematics C at Graz University of Technology

08.2012 - 09.2012 Visiting Scholarship at the University of Sydney

since 03.2016 Lecturer at Technische Hochschule Deggendorf

10.2016 - 04.2017 Data Scientist at Know Center GmbH, Graz

04.2017 - 09.2017 Visiting Professor for Mathematical Statistics at University of Bayreuth

since 10.2017 Assistant Professor at the Institute of Analysis and Number Theory at Graz University of Technology

since 11.2017 Research Assistant at Chair of Stochastics and its Applications at University of Passau

## Research Interests

Random walks (Markov chains) on graphs, groups, free products and regular languages, asymptotic behaviour of random walks (in particular, rate of escape and asymptotic entropy), branching random walks, boundary theory of random walks, statistics.

## Publications

Lorenz Gilch: Effiziente Hermitesche Quantorenelimination: Diploma thesis, University of Passau, 2003.

A. Dolzmann, L. Gilch: Generic Hermitian Quantifier Elimination: Artifical Intelligence and Symbolic Computation, 7th International Conference, AISC 2004, Linz/Austria; Springer-Verlag, September 2004.

Lorenz Gilch: Rate of Escape of Random Walks on Free Products, Journal of Australian Math. Socitey. Volume 83, Part I, pages 31 - 54, 2007.

Lorenz Gilch: Rate of Escape of Random Walks. PhD thesis, Graz University of Technology, 2007.

Lorenz Gilch: Rate of Escape on the Lamplighter Tree, J. Math. Sciences (N.Y.), Volume 156, No. 1, pages 173 - 186, 2009.

Lorenz Gilch: Acceleration of Lamplighter Random Walks, Markov Processes and Related Fields, 14, pages 465 - 486, 2008.

Lorenz Gilch: Rate of Escape of Random Walks on Regular Languages and Free Products by Amalgamation of Finite Groups. Proceedings to 5th Colloquium on Mathematics and Computer Science, Blaubeuren, DMTCS, pages 2544 - 2560, 2008.

Lorenz Gilch, Sebastian Müller: Random Walks on Directed Covers of Graphs. Journal of Theoretical Probability. Volume 24, Issue 1, pages 118 - 149, DOI 10.1007/s10959-009-0256-0, 2011.

Elisabetta Candellero, Lorenz Gilch: Phase Transitions for Random Walk Asymptotics on Free Products of Groups. Random Structures and Algorithms, Vol. 40, Issue 2, 150 - 181, 2012.

Lorenz Gilch: Asymptotic Entropy of Random Walks on Free Products, Electronic Journal of Probability, Volume 16, pages 76 - 105, 2011.

Elisabetta Candellero, Lorenz Gilch and Sebastian Müller: Branching Random Walks on Free Products of Groups, Proc. Lond. Math. Soc. (3) 104, no. 6, pages 1085 - 1120, 2012.

Lorenz Gilch, Francois Ledrappier: Regularity of the Drift and Entropy of Random Walks in Groups, Publ. Mat. Urug., 12. Vol. 14, 147-158, 2013.

Lorenz Gilch and Sebastian Müller: Ends of branching random walks on planar hyperbolic Cayley graphs. In "Groups, Graphs, and Random Walks", (Editors: T.Ceccherini-Silberstein, M.Salvatori and E.Sava-Huss), London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge 2016.

Lorenz Gilch, Sebastian Müller and James Parkinson: Limit theorems for random walks on Fuchsian buildings and Kac-Moody groups, "Groups, Geometry and Dynamics", accepted for publication, 2016.

Lorenz Gilch: Asymptotic Entropy of Random Walks on Regular Languages over a Finite Alphabet, Elect. J. of Probab., Vol. 21, No. 8, 1-42, 2016.

Lorenz Gilch and Sebastian Müller: Counting self-avoiding walks on free products of graphs, Discr. Math. 340, Issue 3, 325--332, 2017.

Lorenz Gilch, Sebastian Müller and James Parkinson: Asymptotic Entropy of Random Walks on Fuchsian Buildings and Kac-Moody Groups, Math. Zeitschrift, Vol. 285, Iss 3-4, 707-738, 2017.

Lorenz Gilch: Asymptotic Properties of Random Walks via Generating Functions, Habilitation thesis, 2016.

Downloads via http://www.math.tugraz.at/~gilch/index.html

## Awards

02.2004 Winner of the Award of the Faculty Price of the Faculty of Mathematics and Informatics of the University of Passau in the category «Diplom-Mathematik»

2013 Nomination for Austrian State Price „Ars docendi – Staatspreis für exzellente Lehre“ by StV Elektrotechnik

## Teaching

**SS 18**

5996V Markov-Ketten

5996UE Markov-Ketten

5262V Mathematik in technischen Systemen II**5270V Vorlesung: Grundlagen der Mathematik II**

## Topics for Bachelor and Master thesis

- Detecting change points in Markov chains; see Article from A. Polansky (http://ai2-s2-pdfs.s3.amazonaws.com/0f3f/c6bb0f2d9a15a15f36e69bd2a4fe8112b799.pdf): Markov chains behave according to some transition matrix. At some known (or unknown) time the transition matrix has been changed. The task is to find out as quickly as possible whether the transition matrix has been changed or not. The above article presents some solutions for these questions. The task is to elaborate and explain the solutions.