Abstract
AbstractWe study a symmetric diffusion process on $\mathbb {R}^{d}$
ℝ
d
, d ≥ 2, in divergence form in a stationary and ergodic random environment. The coefficients are assumed to be degenerate and unbounded but satisfy a moment condition. We derive upper off-diagonal estimates on the heat kernel of this process for general speed measure. Lower off-diagonal estimates are also shown for a natural choice of speed measure, under an additional mixing assumption on the environment. Using these estimates, a scaling limit for the Green function is proven.
Publisher
Springer Science and Business Media LLC
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