Local central limit theorem for diffusions in a degenerate and unbounded random medium

We study a symmetric diffusion X on Rᵈ in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients. We prove a quenched local central limit theorem for X, under some moment conditions on the environment; the key tool is a local parabolic Harnack inequality obtained with Moser iteration technique.