Archive: Stochastik Rhein-Main

Events

Date Category Speakers Title

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. Read more

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