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arXiv · 2001.10740

Quenched local limit theorem for random walks among time-dependent ergodic degenerate weights

Sebastian Andres·Alberto Chiarini·Martin Slowik
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Abstract

We establish a quenched local central limit theorem for the dynamic random conductance model on $\mathbb{Z}^d$ only assuming ergodicity with respect to space-time shifts and a moment condition. As a key analytic ingredient we show H\"older continuity estimates for solutions to the heat equation for discrete finite difference operators in divergence form with time-dependent degenerate weights. The proof is based on De Giorgi's iteration technique. In addition, we also derive a quenched local central limit theorem for the static random conductance model on a class of random graphs with degenerate ergodic weights.

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Sebastian Andres, Alberto Chiarini, Martin Slowik. 2020-01-29. Quenched local limit theorem for random walks among time-dependent ergodic degenerate weights. https://doi.org/10.1007/s00440-021-01028-6

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