Title: Harnack inequality, homogenization and random walks in a degenerate random environment

Date: 12/07/2017

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

Speaker: Xiaoqin Guo, University of Wisconsin-Madison

Stochastic homogenization studies the effective equations or laws that characterize the large scale phenomena for systems with complicated random dynamics at microscopic levels. In this talk, we explore the relation between stochastic homogenization and a probabilistic model called random motion in a random medium. In particular we focus on dynamics on the integer lattice which is non-reversible in time and defined by a non-divergence form linear operator which is non-elliptic. A difficulty in studying this problem is that coefficients of the operator are allowed to be zero. Using random walks in random media, we present a Harnack inequality and a quantitative result for homogenization for this random operator. Joint work with N.Berger (TU-Munich), M.Cohen (Jerusalem) and J.-D. Deuschel (TU-Berlin).