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