Invariance Principle for symmetric Diffusions in a degenerate and unbounded stationary and ergodic Random Medium

Abstract

We study a symmetric diffusion $X$ on ${\mathbb{R}}^d$ in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients $a^{\omega }$. The diffusion is formally associated with $L^{\omega }u=\nabla \cdot (a^{\omega }\nabla u)$, and we make sense of it through Dirichlet forms theory. We prove for $X$ a quenched invariance principle, under some moment conditions on the environment; the key tool is the sublinearity of the corrector obtained by Moser's iteration scheme.

Minor typos corrected