Anomalous Heat Kernel for Random Walks in Random Environments of Conductances

2016/03/21 by Omar Boukhadra, Boukhadra, Omar
Mathematics · Physics and Astronomy · #60G50 #60J10 #60K37 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1603.06323

openalex publication_date 2016/03/21 · openalex created_date 2023/09/14 · openalex updated_date 2026/08/02

Abstract

We study the trapping phenomenon of random walks in random environments of i.i.d. random conductances on the bonds of the grid ℤ^d, the so-called random conductance model. Our main results concern the important model with conductances in [0, 1] and a polynomial-tailed law near zero for which we find the correct order of decay of the anomalous heat kernel for d ≥ 5. In d = 4, the behavior is found to be normal. In addition, we look at the symmetrical situation with conductances in [1, ∞) with a polynomial law at infinity, which also shows opposite return probability behaviors.

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