Sharp threshold for the ballisticity of the random walk on the exclusion process

In this talk, I will overview works on random walks in dynamical random environments. I will recall a result obtained in collaboration with Hilario and Teixeira and then I will focus on a work with Conchon—Kerjan and Rodriguez. Our main interest is to investigate the long-term behavior 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 density but at most one, and that it is strictly monotonic. We will explain how this 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.

• Speaker: Daniel Kious (Bath)
• Tuesday 11 March 2025, 14:00–15:00
• Venue: MR12.
• Series: Probability; organiser: ww295.