Archiv: Stochastik Rhein-Main

13.01.2023 Rhein-Main-Kolloquium

Marcel Ortgiese (University of Bath)

RMKS Frankfurt 13.01.2023

23.06.2023 Rhein-Main-Kolloquium

Mark Sellke (Harvard University)
Steffen Polzer (Université de Genève)

RMKS Darmstadt 23. Juni 2023

07.07.2023 Rhein-Main-Kolloquium

Christoph Czichowsky (London School of Economics and Political Science)
David Prömel (Universität Mannheim)

RMKS Frankfurt 7. Juli 2023

02.06.2023 Rhein-Main-Kolloquium

Torben Krüger (FAU)
Johannes Alt (Universität Bonn)

RMKS Mainz 2. Juni 2023

02.02.2024 Rhein-Main-Kolloquium

Peter Mörters (Universität Köln)
Alessandra Bianchi (Università degli Studi di Padova)

RMKS Frankfurt/Main 02.02.2024

24.11.2023 Rhein-Main-Kolloquium

Véronique Gayrard (HCM Marseille)
Jean-Christophe Mourrat (ENS Lyon)

RMKS 24.11.2023 Mainz

21.06.2024 Rhein-Main-Kolloquium

Stein Andreas Bethuelsen (University of Bergen)

RMK Mainz

Assign to each lattice point of Z^d a Poissonian number of particles and let each of them evolve independently as discrete-time simple random walks. On top of this dynamically evolving environment we consider an additional random walk whose jump transition depends on whether there are particles present at its location or not. This is the so-called random walk on random walks model. Previous studies have concluded that this model on Z^d, d\geq1, has a diffusive scaling when the density of particles is sufficiently low or sufficiently high. We will argue that this holds for all densities for the model on Z^d with d\geq 5. Our proof of this rely on a novel domination result for the dynamic environment that, when combined with coupling arguments and standard random walk estimates, yield uniform mixing bounds for the so-called local environment process. Based on joint work, partly in progress, with Florian Völlering (University of Leipzig) weiterlesen

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. weiterlesen

21.06.2024 Rhein-Main-Kolloquium

Jiří Černý (Universität Basel)

RMK Mainz

In the presentation, I will consider two related models: the one-dimensional branching Brownian motion in random environment (BBMRE), and the randomized F-KPP equation (rFKPP). I will discuss the following natural questions: (1) Given a typical realisation of the environment, are the distributions of the maximal particle of the BBMRE (re-centred around their medians) tight? (2) For the same environment, is the width of the front of the "travelling-wave" solution to rFKPP uniformly bounded in time? Surprisingly, it turns out that the answers to these questions can be different. This highlights that, when compared to the settings of homogeneous branching Brownian motion and the F-KPP equation in a homogeneous environment, the introduction of a random environment leads to a much more intricate behaviour. The presentation is based on joint works with A. Drewitz, L. Schmitz, and P. Oswald. weiterlesen

28.01.2017 Oberseminar Mainz

Marcel Ortgiese (University of Bath)

Ein Vortrag im OS Mainz

25.04.2017 Oberseminar Mainz

Benedikt Jahnel (WIAS Berlin)

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

04.07.2017 Oberseminar Mainz

Roger Tribe (University of Warwick)

Coalescing Random Walks and related models

20.06.2017 Oberseminar Mainz

Carina Zeller

LAMN für ein zweiparametriges, nullrekurrentes Modell

07.11.2017 Oberseminar Mainz

Bjarki Eldon (Museum für Naturkunde, Berlin)

Modeling gene genealogies in highly fecund populations

14.11.2017 Oberseminar Mainz

Fabian Freund (Universität Hohenheim)

The block containing 1 for exchangeable coalescent processes

16.04.2019 Oberseminar Mainz

Sandra Kliem (Goethe-Universität Frankfurt)

Representations for measure-valued branching processes revisited

07.05.2019 Oberseminar Mainz, Rhein-Main-Kolloquium

Cornelia Pokalyuk ((Goethe-Universität Frankfurt/Main))

Cornelia Pokalyuk (Goethe-Universität Frankfurt/Main) TBA

21.05.2019 Oberseminar Mainz

Franz Baumdicker (Princeton University und Universität Freiburg)

Estimating evolutionary rates in the defense memory of the prokaryotic immune system CRISPR

19.06.2019 Oberseminar Mainz

Jiří Černý (Universität Basel)

Zero-mean Gaussian free field on regular graphs

28.05.2019 Oberseminar Mainz

Vlada Limic (Université de Strasbourg)

20 years of the Multiplicative coalescent

Veranstaltungsarchiv

Events

RMKS Frankfurt 13.01.2023

RMKS Darmstadt 23. Juni 2023

RMKS Frankfurt 7. Juli 2023

RMKS Mainz 2. Juni 2023

RMKS Frankfurt/Main 02.02.2024

RMKS 24.11.2023 Mainz

RMK Mainz

RMK Frankfurt

RMK Mainz

Ein Vortrag im OS Mainz

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

Coalescing Random Walks and related models

LAMN für ein zweiparametriges, nullrekurrentes Modell

Modeling gene genealogies in highly fecund populations

The block containing 1 for exchangeable coalescent processes

Representations for measure-valued branching processes revisited

Cornelia Pokalyuk (Goethe-Universität Frankfurt/Main) TBA

Estimating evolutionary rates in the defense memory of the prokaryotic immune system CRISPR

Zero-mean Gaussian free field on regular graphs

20 years of the Multiplicative coalescent

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