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

@article{Andres2020QuenchedLL,
  title={Quenched local limit theorem for random walks among time-dependent ergodic degenerate weights},
  author={Sebastián Andrés and Alberto Chiarini and Martin Slowik},
  journal={Probability Theory and Related Fields},
  year={2020},
  volume={179},
  pages={1145-1181}
}
We establish a quenched local central limit theorem for the dynamic random conductance model on $${\mathbb {Z}}^d$$ 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… 

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