Heat kernel estimates for strongly recurrent random walk on random media

2008/06/27 by Takashi Kumagai, Kumagai, Takashi, Jun Misumi +1 · 1 citation
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0806.4507

openalex publication_date 2008/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish general estimates for simple random walk on an arbitrary infinite random graph, assuming suitable bounds on volume and effective resistance for the graph. These are generalizations of the results in \cite[Section 1,2]BJKS, and in particular, imply the spectral dimension of the random graph. We will also give an application of the results to random walk on a long range percolation cluster.

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• Spectral dimensions for one-dimensional critical long-range percolation

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