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Quenched local limit theorem for random walks among time-dependent ergodic degenerate weights
Sebastian Andres, Alberto Chiarini, Martin Slowik · 2020-01-29 · via math.PR updates on arXiv.org

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 Hölder 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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