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2009 On the domination of a random walk on a discrete cylinder by random interlacements
Alain-Sol Sznitman
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Electron. J. Probab. 14: 1670-1704 (2009). DOI: 10.1214/EJP.v14-679

Abstract

We consider simple random walk on a discrete cylinder with base a large $d$-dimensional torus of side-length $N$, when $d$ is two or more. We develop a stochastic domination control on the local picture left by the random walk in boxes of side-length almost of order $N$, at certain random times comparable to the square of the number of sites in the base. We show a domination control in terms of the trace left in similar boxes by random interlacements in the infinite $(d+1)$-dimensional cubic lattice at a suitably adjusted level. As an application we derive a lower bound on the disconnection time of the discrete cylinder, which as a by-product shows the tightness of the laws of the ratio of the square of the number of sites in the base to the disconnection time. This fact had previously only been established when $d$ is at least 17.

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Alain-Sol Sznitman. "On the domination of a random walk on a discrete cylinder by random interlacements." Electron. J. Probab. 14 1670 - 1704, 2009. https://doi.org/10.1214/EJP.v14-679

Information

Accepted: 25 July 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1196.60170
MathSciNet: MR2525107
Digital Object Identifier: 10.1214/EJP.v14-679

Subjects:
Primary: 60G50
Secondary: 60K35 , 82C41

Keywords: disconnection , discrete cylinders , Random interlacements , Random walks

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