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Homogenization theory of random walks in degenerate random environment

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arxiv 2504.06690 v1 pith:4IXH7B7G submitted 2025-04-09 math.PR

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keywords randomenvironmenthomogenizationlimittheoremswalksalmostcentral
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Recent progress on the understanding of the Random Conductance Model is reviewed. A particular emphasis is on homogenization results such as functional central limit theorems, local limit theorems and heat kernel estimates for almost every realization of the environment, established for random walks among stationary ergodic conductances that are possibly unbounded but satisfy certain moment conditions.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The diffusivity of supercritical Bernoulli percolation is infinitely differentiable

    math.PR 2025-06 conditional novelty 8.0 of 10

    The mapping p to sigma(p) for supercritical bond percolation on Z^d is C^infinity on (p_c,1], a full-interval extension of Kozlov's 1989 result.

  2. Anchored Nash inequalities and heat kernel bounds for a class of random conductance models with long-range jumps

    math.PR 2026-07 accept novelty 7.0 of 10

    Degenerate long-range random conductance models and percolation clusters satisfy on-diagonal heat kernel upper bounds of order t^{-d/2} under explicit moment conditions.

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