Xiaoqin Guo : Einstein relation and steady states for the random conductance model

Posted by Cheng Ouyang , part of the Statistics and Data Science Seminar.

At

Feb. 3, 2016, 4 p.m.

In

SEO 636

Abstract

The Einstein relation describes the relation between the response of a system to a perturbation and its diffusivity at equilibrium. It states that the derivative (with respect to the strength of the perturbation) of the velocity equals the diffusivity. In this talk we consider random walks in iid random conductances on the integer lattice $Z^d$. We show that when $d\ge 3$, the invariant measure for the environment viewed from the particle has a first order expansion in terms of the perturbation. The Einstein relation will follow as a corollary of this expansion. This talk is based on a joint work with N. Gantert and J. Nagel.