Open Access
2008 Random walk on a discrete torus and random interlacements
David Windisch
Author Affiliations +
Electron. Commun. Probab. 13: 140-150 (2008). DOI: 10.1214/ECP.v13-1359


We investigate the relation between the local picture left by the trajectory of a simple random walk on the torus $({\mathbb Z} / N{\mathbb Z})^d$, $d \geq 3$, until $uN^d$ time steps, $u > 0$, and the model of random interlacements recently introduced by Sznitman. In particular, we show that for large $N$, the joint distribution of the local pictures in the neighborhoods of finitely many distant points left by the walk up to time $uN^d$ converges to independent copies of the random interlacement at level $u$.


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David Windisch. "Random walk on a discrete torus and random interlacements." Electron. Commun. Probab. 13 140 - 150, 2008.


Accepted: 10 March 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1187.60089
MathSciNet: MR2386070
Digital Object Identifier: 10.1214/ECP.v13-1359

Primary: 60G50
Secondary: 60K35 , 82C41

Keywords: Random interlacements , Random walk

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