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arXiv · 2011.12731

Lower Gaussian heat kernel bounds for the Random Conductance Model in a degenerate ergodic environment

Sebastian Andres·Noah Halberstam
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Abstract

We study the random conductance model on $\mathbb{Z}^d$ with ergodic, unbounded conductances. We prove a Gaussian lower bound on the heat kernel given a polynomial moment condition and some additional assumptions on the correlations of the conductances. The proof is based on the well-established chaining technique. We also obtain bounds on the Green's function.

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Sebastian Andres, Noah Halberstam. 2020-11-25. Lower Gaussian heat kernel bounds for the Random Conductance Model in a degenerate ergodic environment. https://doi.org/10.1016/j.spa.2021.05.003

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