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
Sommersemester 2024:
Stochastik I
Ergänzungsvorlesung Stochastische Populationsmodelle
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 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.
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
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
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