Internal DLA on cylinder graphs: fluctuations and mixing

2019/09/21 by Silvestri, Vittoria · 2 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1909.09893

Abstract

We use coupling ideas introduced in \citelevine2018long to show that an IDLA process on a cylinder graph G× ℤ forgets a typical initial profile in O( N√(τ_N) (log N)² ) steps for large N, where N is the size of the base graph G, and τ_N is the total variation mixing time of a simple random walk on G. The main new ingredient is a maximal fluctuations bound for IDLA on G× ℤ which only relies on the mixing properties of the base graph G and the Abelian property.

Cited by

• Internal Diffusion Limited Aggregation with Critical Branching Random Walks
• Construction of ergodic IDLA forests in ℤ^d

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