Invariance Principle for symmetric Diffusions in a degenerate and unbounded stationary and ergodic Random Medium.
Alberto Chiarini, Jean‐Dominique Deuschel · 2014
We study a symmetric diffusion X on Rd in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients aω. The diffusion is formally associated with Lωu = ∇ ?(aωu), 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.