Non-uniformly parabolic equations and applications to the random conductance model

2020/09/24 by Bella, Peter, Schäffner, Mathias · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2009.11535

Abstract

We study local regularity properties of linear, non-uniformly parabolic finite-difference operators in divergence form related to the random conductance model on \mathbb Z^d. In particular, we provide an oscillation decay assuming only certain summability properties of the conductances and their inverse, thus improving recent results in that direction. As an application, we provide a local limit theorem for the random walk in a random degenerate and unbounded environment.

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• Scaling limit of the discrete Gaussian free field with degenerate random conductances

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