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 Electronic Communications in Probability > Vol. 13 (2008) > Paper 14 open journal systems 


Random walk on a discrete torus and random interlacements

David Windisch, ETH Zurich


Abstract
We investigate the relation between the local picture left by the trajectory of a simple random walk on the torus (Z/NZ)d, d ≥ 3, until u Nd 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 u Nd converges to independent copies of the random interlacement at level u.


Full text: PDF

Pages: 140-150

Published on: March 10, 2008
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Electronic Communications in Probability. ISSN: 1083-589X