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2019 Growing in time IDLA cluster is recurrent
Ruojun Huang
Electron. Commun. Probab. 24: 1-11 (2019). DOI: 10.1214/19-ECP233

Abstract

We show that Internal Diffusion Limited Aggregation (IDLA )on $\mathbb{Z} ^{d}$ has near optimal Cheeger constant when the growing cluster is large enough. This implies, through a heat kernel lower bound derived previously in [11], that simple random walk evolving independently on growing in time IDLA cluster is recurrent when $d\ge 3$.

Citation

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Ruojun Huang. "Growing in time IDLA cluster is recurrent." Electron. Commun. Probab. 24 1 - 11, 2019. https://doi.org/10.1214/19-ECP233

Information

Received: 16 January 2019; Accepted: 16 April 2019; Published: 2019
First available in Project Euclid: 13 June 2019

zbMATH: 07068655
MathSciNet: MR3962481
Digital Object Identifier: 10.1214/19-ECP233

Subjects:
Primary: 60K37, 82C24
Secondary: 60K35

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