Shalin Parekh
University of Maine
Title
Extremal Scaling limits for random walks in space-time random media
Abstract
We introduce a family of random walks in space-time random environments, and we study the scaling limits of these models in several different scaling regimes in all spatial dimensions. We show that each regime gives rise to a different limiting stochastic PDE. More precisely, at large time and space scales, there are Gaussian fluctuations up to a certain specific spatial centering radius in the tail of the quenched probability distribution of the random walk, which we call the critical scale. This critical scale depends on the underlying spatial dimension. We conjecture that the fluctuations are no longer Gaussian at the critical scale, which we already proved in d=1, with ongoing progress in d=2. Based on joint works with Hindy Drillick, Sayan Das, Federico Sau, Jonathan Wang Hou.