Archive: Stochastik Rhein-Main

Alison Etheridge (University of Oxford)
Jan Swart (UTIA Prague)
Nic Freeman (University of Sheffield)
Félix Foutel-Rodier (University of Oxford)
Andreas Greven (FAU Erlangen-Nürnberg)

Spring School 2023

15.11.2019 Rhein-Main-Kolloquium

Sarah Penington (Bath)
Amandine Véber (Paris)

RMK 15.11.2019 JGU Mainz: Amandine Véber (Paris) und Sarah Penington (Bath)

03.02.2023 Rhein-Main-Kolloquium

Amaury Lambert (Collège de France und École Normale Supérieure, Paris)
Emmanuel Schertzer (Universität Wien)

RMKS Mainz 03.02.2023

27.01.2017 Rhein-Main-Kolloquium

Amine Asselah (Université Paris-Est)
Yvan Velenik (Universität Genf)

RMK Frankfurt Winter 2016/17

18.07.2023 Oberseminar Mainz

Andreas Klippel (TU Darmstadt)

Comparison of the random loop model to percolation and infinite loops in the random link model

14.01.2022 Rhein-Main-Kolloquium

René Schilling (TU Dresden)

RMK Mainz ONLINE

08.06.2021 Oberseminar Mainz

Andreas Meier (Johannes Gutenberg-Universität Mainz)

Oberseminar Stochastik

12.07.2024 Rhein-Main-Kolloquium

Nicolas Champagnat (Nancy)
Anita Winter (Duisburg-Essen)

RMK Frankfurt

The grapheme-valued Wright-Fisher Diffusion with mutation --- In Athreya, den Hollander and Röllin (2021) models from population genetics were used to de fine 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) -------------------------------------------------------------------- Scaling limits of individual-based models in adaptive dynamics and local extinction of populations (N. Champagnat) --- 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. Read more

19.–23.03.2018 Sommer-/Winterschule

Hugo Duminil-Copin (Univerite de Geneve / IHES Paris)
Roland Bauerschmidt (University of Cambridge)
Roman Kotecky (University of Warwick)
Margherita Disertori (Universität Bonn)
Aran Raoufi (Univeriste de Geneve)
Igor Kortchemski (ENS Paris)
Antti Knowles (Université de Genève)

Spin Systems - Discrete and Continuous

12.06.2025 Oberseminar Darmstadt

Bas Lodewijks (Universität Augsburg)

Preferential Attachment trees with Vertex Death: Persistence of the Maximum Degree

25.04.2017 Oberseminar Mainz

Benedikt Jahnel (TU Braunschweig)

The Widom-Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality

Events archive

Events

Some random interfaces in statistical mechanics

RMK Frankfurt

Extreme value theory for variable-speed branching Brownian motion

Random Walk among Moving Traps

RMK Darmstadt

Potts model at the transition point: continuity vs wetting

RMK Darmstadt

RMK Mainz

Macroscopic loops in interacting random walk loop soups

Spring School 2023

RMK 15.11.2019 JGU Mainz: Amandine Véber (Paris) und Sarah Penington (Bath)

RMKS Mainz 03.02.2023

RMK Frankfurt Winter 2016/17

Comparison of the random loop model to percolation and infinite loops in the random link model

RMK Mainz ONLINE

Oberseminar Stochastik

RMK Frankfurt

Spin Systems - Discrete and Continuous

Preferential Attachment trees with Vertex Death: Persistence of the Maximum Degree

The Widom-Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality

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