Percolation Today is an online seminar aiming to promote the exchange of exciting new ideas on both Bernoulli and dependent percolation processes, at a level appropriate for specialists in the area. We hope to be a focal point to foster new connections and collaborations between the global community of percolation lovers.
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Sharp threshold for the ballisticity of the random walk on the exclusion process
Speakers: Daniel Kious and Guillaume Conchon-Kerjan
Date: April,14th / 16:00 CEST
Abstract: In this double talk, we will start with an overview on random walks in dynamical random environments, outlining the difficulties and the canonical properties of the model. We will notably present results by Kious, Hilário and Teixeira (2020) and a more recent result by Conchon-Kerjan, Kious and Rodriguez. Our main interest is to investigate the long-term behaviour of a random walker evolving on top of the simple symmetric exclusion process (SSEP) at equilibrium, with density in [0,1]. At each jump, the random walker is subject to a drift that depends on whether it is sitting on top of a particle or a hole. We prove that the speed of the walk, seen as a function of the density, exists for all densities but at most one, and that it is strictly monotonic. We will explain how this last part can be seen as a sharpness result and provide an outline of the proof, whose general strategy is inspired by techniques developed for studying the sharpness of strongly-correlated percolation models, such as the level-sets of the GFF.
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Organizers:
Barbara Dembin
Piet Lammers
Hugo Vanneuville
Franco Severo
Scientific Commitee:
Christophe Garban
Tom Hutchcroft
Pictures by: Adèle Ivain and Laurie Quétel