Joint colloquium of the probability and statistics workgroups

TU Darmstadt / Goethe-Universität Frankfurt / Gutenberg-Universität Mainz

Summer Term 2024

Friday, June 21st, 2024 - JGU Mainz, 15 c.t., Hilbertraum (05-432)

15:15 Andreas Bethuelsen (University of Bergen)

Random walk on random walks in high dimensions: non-perturbative results

Abstracts see past events / Abstracts siehe bei vergangene Veranstaltungen unten

Tightness of the maximum of branching Brownian motion in random environment and fronts of randomized F-KPP equation.

Abstracts see past events / Abstracts siehe bei vergangene Veranstaltungen unten

Friday, July 12th, 2024 - GU Frankfurt/Main, 15 c.t.

7. OG, Raum 711 groß, Campus Bockenheim, Robert-Mayer-Straße 10, Frankfurt am Main

15:15: Prof. Anita Winter (Duisburg-Essen)

Grapheme-valued Wright-Fisher diffusion with mutation

In Athreya, den Hollander and Röllin (2021) models from population genetics were used to define stochastic dynamics in the space of graphons that arise as continuum limits of dense graph sequencess. In this talk we extend this framework to a model with mutation. In particular, we define a finite graph valued Markov chain that can be associated with the infinite many alleles model, and establish a diffusion limit as the number of vertices goes to infinity. For that we encode finite graphs as graphemes. Graphems are those graphons that can be represented as a triple consisting of a topological vertex space, an adjacency matrix and a sampling measure. The space of graphons is equipped with convergence of sample subgraph densities.
(joint work with Andreas Greven, Frank den Hollander and Anton Klimovsky)

16:15 Coffee break

16:45: Prof. Nicolas Champagnat (Nancy)

Scaling limits of individual-based models in adaptive dynamics and local extinction of populations

Starting from an individual-based birth-death-mutation-selection model of adaptive dynamics with three scaling parameters (population size, mutation rate, mutation steps size), we will describe several scaling limits that can be applied to this model to obtain macroscopic models of different natures (PDE, Hamilton-Jacobi equation, stochastic adaptive walks, canonical equation of adaptive dynamics), which allow to characterize the long-term evolution of the population. Motivated by biological criticisms on the time-scale of evolution and the absence of local extinctions in the obtained macroscopic models, we propose new parameter scalings under which we can characterize the evolution of population sizes of the order of K\beta$, where K is the order of magnitude of the total population size, and which allows for local extinction of subpopulations.

This presentation will gather results obtained with several collaborators: Régis Ferrière, Sylvie Méléard, Amaury Lambert, Viet Chi Tran, Sepideh Mirrahimi, Vincent Hass.

Winter Term 2024/2025

Friday, November 15th, 2024 - GU Frankfurt/Main, 15 c.t. - Raum NG 1.741a, Campus Westend, Frankfurt am Main

Christina Goldschmidt (Oxford)

Benedikt Stufler (TU Wien)

Friday, November 15th, 2024 - TU Darmstadt, 15 c.t.

Yvan Velenik (Genf)

Alexander Glazman (Innsbruck)

Wegbeschreibungen / Venue:

zur Anreise an die Uni Mainz finden Sie unter https://www.mathematik.uni-mainz.de/anfahrt/,

zur Anreise an die Uni Frankfurt unter https://www.uni-frankfurt.de/38074653/campus_bockenheim und https://www.uni-frankfurt.de/38093742/Campus_Bockenheim-pdf.pdf,

zur Anreise an die TU Darmstadt unter http://www3.mathematik.tu-darmstadt.de/fb/mathe/wir-ueber-uns/adresse-und-lageplan/anreise.html

Termine in früheren Semestern finden Sie hier / for past events please click here.

stochastik@uni-mainz.de