Johannes-Gutenberg-Universität

Institut für Mathematik

Fachbereich 08 – Physik, Mathematik und Informatik

Staudingerweg 9

55099 Mainz

Email: birkner@mathematik.uni-mainz.de

Tel.: 06131/39-23601

Fax : 06131/39-20916

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

Sprechstunde: nach Vereinbarung

Wintersemester 2024/2025:

Stochastik II und Ergänzung Ausgewählte Kapitel der Stochastik

Biostatistik

~~Seminar Erzeugende Funktionen~~

Lehre in vergangenen Semestern

Bursts of coalescence within population pedigrees whenever big families occur (with Dimitrios Diamantidis, Wai-Tong (Louis) Fan and John Wakeley), Genetics 227(1), (2024), doi: 10.1093/genetics/iyae030, biorXiv:2023.10.17.562743

The joint fluctuations of the lengths of the Beta($2-\alpha,\alpha$)-coalescents (with Iulia Dahmer, Christina S. Diehl and Götz Kersting), Ann. Appl. Probab. 34(1A), 277-317 (2024). DOI: 10.1214/23-AAP1964

Local limit theorems for a directed random walk on the backbone of a supercritical oriented percolation cluster (with Stein Andreas Bethuelsen, Andrej Depperschmidt and Timo Schlüter), Electron. J. Probab. 28, Paper No. 37, 54 p. (2023). DOI: 10.1214/23-EJP924

The dynamics of Pareto distributed wealth in a small open economy (with Niklas Scheuer and Klaus Wälde), Econ. Theory 76, No. 2, 607-644 (2023). DOI:10.1007/s00199-022-01471-z

Ancestral lineages in spatial population models with local regulation (with Nina Gantert), in: Probabilistic Structures in Evolution (E. Baake and A. Wakolbinger, eds.), EMS Press, Berlin, 2021, pp. 291-310. arXiv:1912.02558

Genealogies and inference for populations with highly skewed offspring distributions (with Jochen Blath), in: Probabilistic Structures in Evolution (E. Baake and A. Wakolbinger, eds.), EMS Press, Berlin, 2021, pp. 151-178. arXiv:1912.07977

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 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.
(DOI:10.1007/s00440-009-0235-5, 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, Probab. Theory Relat. Fields 187, No. 1-2, 523-569 (2023),
DOI:https://doi.org/10.1007/s00440-023-01212-w.

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.

http://publikationen.ub.uni-frankfurt.de/volltexte/2003/314/

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.

Pair coalescence times of ancestral lineages of two-dimensional logistic branching random walks (with Andrej Depperschmidt and Timo Schlüter), arXiv:2405.02090

Quenched CLT for ancestral lineages of logistic branching random walks (with Andrej Depperschmidt and Timo Schlüter), arXiv:2403.08567

On the fixation probability of an advantageous allele in a population with skewed offspring distribution (with Florin Boenkost, Iulia Dahmer and Cornelia Pokalyuk), arXiv:2310.09045

Survival and complete convergence for a branching annihilating random walk (with Alice Callegaro, Jiří Černý, Nina Gantert and Pascal Oswald), arXiv:2304.09127. To appear in Ann. Appl. Probab.

Collective vs. individual behaviour for sums of i.i.d. random variables: appearance of the one-big-jump phenomenon (with Quentin Berger and Linglong Yuan), arXiv:2303.12505. To appear in Ann. Fac. Sci. Toulouse

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

An updated version is
"A functional CLT for the occupation time of state-dependent
branching random walk",
math.PR/0702020.

17th German probability and statistics days, Stochastiktage Dresden, 11-14 March 2025

11th World Congress in Probability and Statistics, August 12-16, 2024, Bochum

Stochastic Processes in Evolutionary Biology, 20-24 May 2024, Centre international de recontres mathématiques, Luminy

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.

Conference volume (co-edited with Rongfeng Sun and Jan Swart):
Lecture Notes Series, Volume 38, Institute for Mathematical Sciences, National University of Singapore,
World Scientific, 2020. DOI:10.1142/11439

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

IQCB Institute for Quantitative and Computational Biosciences, JGU Mainz
m^{3}odel Mainz Institute of Multiscale Modeling

Seminar series "SPIELE" - Stochastic Processes in EvoLution and Ecology

DFG-Schwerpunkt 2265
Random Geometric Systems

DFG-Schwerpunkt 1590
Probabilistic Structures in Evolution

The Cost of Knowledge

Matthias Birkner Last modified: Mai 2024