A lower bound for disconnection by random interlacements

2013/10/31 by Xinyi Li, Alain-Sol Sznitman · 3 citations
Mathematics · Physics and Astronomy · #math.PR #math-ph #math.MP #msc:60F10 #msc:60K35 #msc:60J27

paper · pdf · doi:10.1214/ejp.v19-3067

published as Electron. J. Probab., 19(17), 1-26, 2014 · 28 pages, appeared in the Electronic Journal of Probability

arxiv created 2014/03/17 · arxiv updated 2014/03/18

Abstract

We consider the vacant set of random interlacements on Z^d, with d bigger or equal to 3, in the percolative regime. Motivated by the large deviation principles obtained in our recent work arXiv:1304.7477, we investigate the asymptotic behavior of the probability that a large body gets disconnected from infinity by the random interlacements. We derive an asymptotic lower bound, which brings into play tilted interlacements, and relates the problem to some of the large deviations of the occupation-time profile considered in arXiv:1304.7477.

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