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2020 Internal DLA on cylinder graphs: fluctuations and mixing
Vittoria Silvestri
Electron. Commun. Probab. 25: 1-14 (2020). DOI: 10.1214/20-ECP339

Abstract

We use coupling ideas introduced in [13] to show that an IDLA process on a cylinder graph $G\times {\mathbb {Z}} $ forgets a typical initial profile in $\mathcal {O}( N\sqrt {\tau _{N}} (\log \! N)^{2} )$ steps for large $N$, where $N$ is the size of the base graph $G$, and $\tau _{N}$ 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 $G\times \mathbb {Z}$ which only relies on the mixing properties of the base graph $G$ and the Abelian property.

Citation

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Vittoria Silvestri. "Internal DLA on cylinder graphs: fluctuations and mixing." Electron. Commun. Probab. 25 1 - 14, 2020. https://doi.org/10.1214/20-ECP339

Information

Received: 2 April 2020; Accepted: 21 July 2020; Published: 2020
First available in Project Euclid: 12 August 2020

zbMATH: 07252781
Digital Object Identifier: 10.1214/20-ECP339

Subjects:
Primary: 60J05

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