Matthias Birkner

Professor für Wahrscheinlichkeitstheorie


Institut für Mathematik
Fachbereich 08 – Physik, Mathematik und Informatik
Staudingerweg 9
55099 Mainz

Tel.: 06131/39-23601
Fax : 06131/39-20916

Büro: Raum 05-623, 5.OG, Staudingerweg 9

Sprechstunde: nach Vereinbarung


Coalescing directed random walks on the backbone of a 1+1-dimensional oriented percolation cluster converge to the Brownian web (with Nina Gantert and Sebastian Steiber), ALEA Lat. Am. J. Probab. Math. Stat. 16, 1029-1054, (2019).

Low-dimensional lonely branching random walks die out (with Rongfeng Sun), Ann. Probab. 47 (2), 774-803, (2019). arXiv:1708.06377

Coalescent results for diploid exchangeable population models (with Huili Liu and Anja Sturm), Electronic Journal of Probability 23 (2018), paper no. 49, 44 pp. arXiv:1709.02563

One-dimensional random walks with self-blocking immigration (with Rongfeng Sun), Ann. Appl. Probab. 27, 109-139, (2017). arXiv:1410.4344.

Random walks in dynamic random environments and ancestry under local population regulation (with Jiří Černý and Andrej Depperschmidt), Electronic Journal of Probability 21 (2016), paper no. 38, 1-43.

Can the site-frequency spectrum distinguish exponential population growth from multiple-merger coalescents? (with Bjarki Eldon, Jochen Blath and Fabian Freund), Genetics 199, no. 3 (2015), 841-856, doi:10.1534/genetics.114.173807

Non-periodic systems with continuous diffraction measures (with Michael Baake and Uwe Grimm), in Mathematics of aperiodic order, Prog. Math. Phys. 309 (2015), 1-32. arXiv:1502.05122

Statistical properties of the site-frequency spectrum associated with Lambda-coalescents (with Jochen Blath and Bjarki Eldon), Genetics 195, no. 3 (2013), 1037-1053. arXiv:1305.6043.

Directed random walk on an oriented percolation cluster (with Jiří Černý, Andrej Depperschmidt and Nina Gantert), Electronic Journal of Probability 18 (2013), Article 80.

Analysis of DNA sequence variation within marine species using Beta-coalescents (with Matthias Steinrücken and Jochen Blath), Theor. Pop. Biol. 87 (2013), 15-24. (preprint version, arXiv:1209.0813)

An ancestral recombination graph for diploid populations with skewed offspring distribution (with Jochen Blath and Bjarki Eldon), Genetics 193, no. 1 (2013), 255-290. arXiv:1203.4950

Collision local time of transient random walks and intermediate phases in interacting stochastic systems (with Andreas Greven and Frank den Hollander), Electronic Journal of Probability 16 (2011), 552-586.

Importance sampling for Lambda-coalescents in the infinitely many sites model (with Jochen Blath, Matthias Steinrücken), Theor. Pop. Biology 79 (2011), 155-173. arXiv:1105.1836

Disorder relevance for the random walk pinning model in dimension 3 (with Rongfeng Sun), Annales de l'Institut Henri Poincaré 47 (2011), 259-293. Available as pdf, arxiv:0912.1663.

Quenched LDP for words in a letter sequence (with Andreas Greven and Frank den Hollander), Probability Theory and Related Fields 148, no. 3/4 (2010), 403-456. (WIAS preprint 1349, arxiv:0807.2611) The proof of the representation of the rate function for the case when the mean word length is infinite given in this paper requires amendment, see the Erratum.

Annealed vs quenched critical points for a random walk pinning model (with Rongfeng Sun), Annales de l'Institut Henri Poincaré 46 (2010), 414-441. Available as pdf.

Diffraction of stochastic point sets: Exactly solvable examples (with Michael Baake and Robert V. Moody), Communications in Mathematical Physics 293, no. 3, (2010), 611-660.

Rescaled stable generalised Fleming-Viot processes: Flickering random measures (with Jochen Blath), Electronic Journal of Probability 14 (2009), 2418-2437.

Measure-valued diffusions, general coalescents and population genetic inference (with Jochen Blath), in J. Blath, P. Mörters, M. Scheutzow (Eds.), Trends in Stochastic Analysis, LMS 351, Cambridge University Press, 329-363 (2009). (The preprint version can be found here).

A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks (with Jochen Blath, Martin Möhle, Matthias Steinrücken and Johanna Tams), ALEA Lat. Am. J. Probab. Math. Stat. 6, (2009).

Computing likelihoods for coalescents with multiple collisions in the infinitely-many-sites model (with Jochen Blath), J. Math. Biol. 57, no. 3, (2008), 435-465. Available as pdf (513 kB).

Conditional large deviations for a sequence of words, Stochastic Process. Appl. 118, no. 5, (2008), 703-729. (WIAS preprint 1072, or here for an updated version of that preprint)

A functional CLT for the occupation time of state-dependent branching random walk (with Iljana Zähle), Ann. Probab. 35, no. 6, (2007), 2063-2090. Available as pdf (278 kB).

Survival and complete convergence for a spatial branching system with local regulation (with Andrej Depperschmidt), Ann. Appl. Probab. 17, no. 5/6, (2007), 1777-1807. Available as pdf (320 kB).

Alpha-stable Branching and Beta-Coalescents (with Jochen Blath, Marcella Capaldo, Alison Etheridge, Martin Möhle, Jason Schweinsberg, Anton Wakolbinger). Electronic Journal of Probability 10 (2005), 303-325.

Comparison results and steady states for the Fujita equation with fractional Laplacian (with J.A. López Mimbela, A. Wakolbinger). Ann. Inst. H. Poincaré Anal. Non Linéaire 22, no. 1, (2005), 83-97. (ESI preprint 1265, math.AP/0302353).

A Condition for Weak Disorder for Directed Polymers in Random Environment, Electronic Communications in Probability 9 (2004), 22-25.

Branching processes in random environment - a view on critical and subcritical cases (with Jochen Geiger and Götz Kersting), in the proceedings of the DFG-Schwerpunktprogramm ``Interacting Stochastic Systems of High Complexity''. Available as pdf (236 kB).

Particle systems with locally dependent branching: long-time behaviour, genealogy and critical parameters, PhD thesis, Johann Wolfgang Goethe-Universität Frankfurt, 2003.

Blow-up of semilinear pde's at the critical dimension. A probabilistic approach (with J.A. López Mimbela, A. Wakolbinger). Proc. Amer. Math. Soc. 130 (2002), 2431-2442.

A comparison of free branching and stepping stone models (with A. Wakolbinger). Stochastic models (Ottawa, ON, 1998), 15-23, CMS Conf. Proc., 26.


A quenched large deviation principle in a continuous scenario (with Frank den Hollander), arXiv:1312.2521.

Inference for $\Lambda$-coalescents (with Jochen Blath), WIAS preprint 1211.

Temporal decorrelation for branching random walks with state dependent branching rate, WIAS preprint 1202.

Functional central limit theorem for the occupation time of the origin for branching random walks in d ≥ 3 (with Iljana Zähle), WIAS preprint 1011.
An updated version is "A functional CLT for the occupation time of state-dependent branching random walk", math.PR/0702020.


Wintersemester 2022/2023:
Ergänzungsvorlesung Stochastische Modelle der Populationsbiologie, mit Übung
Seminar Erzeugende Funktionen

Sommersemester 2022:
Stochastik III
Statistik für Informatiker
Hauptseminar Räumliche Stochastische Populationsmodelle (mit Dormanz)

Wintersemester 2021/2022:
Stochastik II
Hauptseminar Irrfahrten in zufälliger Umgebung

Sommersemester 2021:
Stochastik I
Statistik für Informatiker
Hauptseminar Stochastische Modelle der Evolution

Wintersemester 2020/2021:
Grundlagen der Stochastik: Einführung in die Stochastik und Stochastik-Praktikum
Hauptseminar Markovketten und Mischungszeiten

Sommersemester 2020:
Ergänzungsvorlesung Statistische Mechanik von Gittersystemen
Hauptseminar Pinning-Modelle mit Unordnung

Wintersemester 2019/2020:
Ergänzungsvorlesung Statistik

Sommersemester 2019:
Ergänzungsvorlesung Markovketten und -prozesse: Beispiele und Anwendungen
Statistik für Informatiker

Sommersemester 2018:
Stochastik III
Statistik für Informatiker
Hauptseminar Schramm-Loewner-Evolution

Wintersemester 2017/2018:
Stochastik II
Hauptseminar Zufällige Graphen

Sommersemester 2017:
Stochastik I
Statistik für Informatiker
Hauptseminar Pinning-Modelle mit Unordnung

Wintersemester 2016/2017:
Grundlagen der Stochastik: Einführung in die Stochastik und Stochastik-Praktikum
Ergänzungsvorlesung Markovketten und -prozesse: Beispiele und Anwendungen

Sommersemester 2016:
Stochastik III
Hauptseminar Irrfahrten, Bäume und Netzwerke

Wintersemester 2015/2016:
Ergänzungsvorlesung Stochastische Modelle der Populationsbiologie
Hauptseminar Markovketten und Mischungszeiten

Sommersemester 2015:
Stochastik III, Ergänzung Ausgewählte Kapitel der Stochastik
Hauptseminar Irrfahrten in zufälliger Umgebung

Wintersemester 2014/2015:
Stochastik II
Ergänzungsvorlesung Große Abweichungen
Hauptseminar Erweiterungen des linearen Regressionsmodells

Wintersemester 2013/2014:
Grundlagen der Stochastik: Einführung in die Stochastik und Stochastik-Praktikum

Sommersemester 2013:
Stochastische Modelle der Populationsbiologie

Wintersemester 2012/2013:
Hauptseminar Stochastische Modelle der Evolutionsbiologie

Sommersemester 2012:
Stochastik III
Hauptseminar Stochastische Prozesse auf Graphen

Wintersemester 2011/2012:
Stochastik II

Sommersemester 2011:
Stochastik I

Wintersemester 2010/2011:

Folien des Vortrags anläßlich der Betreuten Informationsveranstaltung für Schülerinnen und Schüler der Oberstufe sowie andere Studieninteressierte (BISS), JGU Mainz, 23.6.2010.

Sommersemester 2010:
Große Abweichungen, Spezialvorlesung, Universität Mainz
Zufällige Polymere, Hauptseminar, Universität Mainz

Wintersemester 2009/2010:
Stochastische Modelle der Populationsbiologie, Universität Mainz

Sommersemester 2009:
Statistik für Biologen, Universität München.
Population Genetics, Universität München.

Sommersemester 2008:
Vorlesung "Angewandte Stochastik", Universität Bonn.
Seminar "Kombinatorische Stochastische Prozesse", Universität Bonn. Ankündigungstext.

Sommersemester 2007: Stochastic models from population biology at TU Berlin.

Wintersemester 2005/2006: Mathematik I für Brauerei- und Brennereitechnologen, TU Berlin (in german). More information can be found here.

Sommersemester 2005: "Stochastic models from population biology" at TU Berlin. The announcement (in german) can be found here, a version of the course notes is here.


Workshop Branching and interacting particle systems, 27 February - 2 March 2023, JGU Mainz

Workshop on Probability and Evolution, 4-5 July 2022, Goethe University Frankfurt

Miniworkshop Multiple merger coalescents: population models and inference, 2-4 September 2019, JGU Mainz

Genealogies of Interacting Particle Systems, 17 July - 18 August 2017, Institute for Mathematical Sciences, National University of Singapore

Spring School Geometric Models in Probability, 4 - 8 April 2016, TU Darmstadt

37th Conference on Stochastic Processes and their Applications, 28 July - 1 August 2014, Universidad de Buenos Aires

Mini-Workshop Multiple merger coalescents in population genetics, 28-29 November 2013, JGU Mainz

10th German probability and statistics days, Stochastiktage Mainz, 6-9 March 2012

VIII. YEP-Workshop on Stochastic Models for Population Dynamics, 14-18 March 2011, Eurandom, Eindhoven

Arbeitsgruppe Stochastik   Institut für Mathematik   Johannes-Gutenberg-Universität Mainz   Rhein-Main-Kolloquium Stochastik   Stochastik Rhein-Main

DFG-Schwerpunkt 2265 Random Geometric Systems
DFG-Schwerpunkt 1590 Probabilistic Structures in Evolution

The Cost of Knowledge

Matthias Birkner
Last modified: Okt. 2021