Abstract
We study a symmetric diffusion process on \(\mathbb {R}^{d}\), 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.
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With many thanks to Sebastian Andres for valuable discussions and guidance on this project.
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Taylor, P.A. Off-Diagonal Heat Kernel Estimates for Symmetric Diffusions in a Degenerate Ergodic Environment. Potential Anal 59, 1425–1448 (2023). https://doi.org/10.1007/s11118-022-10007-y
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DOI: https://doi.org/10.1007/s11118-022-10007-y