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Random walk on a discrete torus and random interlacements


 
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1. Title Title of document Random walk on a discrete torus and random interlacements
 
2. Creator Author's name, affiliation, country David Windisch; ETH Zurich
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random walk; random interlacements
 
3. Subject Subject classification 60G50; 60K35; 82C41
 
4. Description 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 $u$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2008-03-10
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1359
 
10. Identifier Digital Object Identifier 10.1214/ECP.v13-1359
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 13
 
12. Language English=en
 
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