## Electronic Communications in Probability

### Random walk on a discrete torus and random interlacements

David Windisch

#### Abstract

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 $u$.

#### Article information

Source
Electron. Commun. Probab., Volume 13 (2008), paper no. 14, 140-150.

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

https://projecteuclid.org/euclid.ecp/1465233441

Digital Object Identifier
doi:10.1214/ECP.v13-1359

Mathematical Reviews number (MathSciNet)
MR2386070

Zentralblatt MATH identifier
1187.60089

Keywords
Random walk random interlacements

Rights

#### Citation

Windisch, David. Random walk on a discrete torus and random interlacements. Electron. Commun. Probab. 13 (2008), paper no. 14, 140--150. doi:10.1214/ECP.v13-1359. https://projecteuclid.org/euclid.ecp/1465233441

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