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Random walk on a discrete torus and random interlacements

   
@article{ECP1359,
	author = {David Windisch},
	title = {Random walk on a discrete torus and random interlacements},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {13},
	year = {2008},
	keywords = {Random walk; random interlacements},
	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 $u$.},
	pages = {no. 14, 140-150},
	issn = {1083-589X},
	doi = {10.1214/ECP.v13-1359},    
        url = {http://ecp.ejpecp.org/article/view/1359}}