Weak Convergence for Reversible Random Walks in a Random Environment

Abstract

Assign to each edge $e$ of the square lattice $\mathbb{Z}^2$ a random bond conductivity $c(e)$. If $c(e)$ are stationary, ergodic and such that $0 < a < c(e) < b < \infty$ for all edges $e$, then there is a central limit theorem for the corresponding reversible random walk on the lattice which holds for almost all environments.