Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact 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.mp4Date: Tuesday, March 27, 2018Time: 1:30 pmLocation: Wean Hall 7218Submitted by:  Ian Tice