Growing in time IDLA cluster is recurrent

2018/09/28 by Ruojun Huang, Huang, Ruojun
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1809.11022

Abstract

We show that Internal Diffusion Limited Aggregation (IDLA) on ℤ^d has near optimal Cheeger constant when the growing cluster is large enough. This implies, through a heat kernel lower bound derived previously in [H], that simple random walk evolving independently on growing in time IDLA cluster is recurrent when d≥ 3.

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