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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Xiaoqin Guo
UW Madison
Title: Quantitative homogenization and Harnack inequality for a non-elliptic balanced random environment

Abstract: In the d-dimensional integer lattice $\mathbb Z^d$, $d\ge 2$, we consider a discrete non-divergence form difference operator $$ L_a u(x)=\sum_{i=1}^d a_i(x)[u(x+e_i)+u(x-e_i)-2u(x)] $$ where $a(x)=diag(a_1(x),..., a_d(x)), x\in\mathbb Z^d$ are random nonnegative diagonal matrices which are independent and identically distributed. A difficulty in studying this problem is that eigenvalues of $a(x)$ are allowed to be zero. In this talk, using random walks in random media and its percolative structure, we present a Harnack inequality and quantitative homogenization result for this random operator. Joint work with N.Berger, M.Cohen and J.-D. Deuschel.

Recording: http://mm.math.cmu.edu/recordings/cna/xiaoqin_guo_small.mp4
Date: Tuesday, March 27, 2018
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice