Time：11:00-12:00, Friday, October 30 2026
Venue：E14-301
Speaker：Hendri Elad Altman, Université Sorbonne Paris Nord
Title：Scaling limit results for line models in heavy-tailed environment
Abstract：Line Models are an example of random walk in random environment on the 2-dimensional lattice with vertical (resp. horizontal) jump rates that are constant along vertical (resp. horizontal) lines. When the environment, or part of it, is heavy-tailed, we expect the walk to become superdiffusive with a singular scaling, and a non-trivial scaling limit.
I will present results obtained with Jean-Dominique Deuschel (TU Berlin) that, for appropriate values of the tail exponents of the environment, show non-explosion for the walk, as well as a scaling limit result when the environment is heavy-tailed in only one direction: the limit is then described as a 2-dimensional Brownian motion, time-changed in one direction by a Kesten-Spitzer process. I will also mention conjectures about the case of a completely heavy-tailed environment.
