Cover levels and random interlacements

Details Cover levels and random interlacements Cover levels and random interlacements

2011-03-10

arxiv.org/abs/1103.2072v1

Mathematics

Probability

21 pages, accepted for publication in Ann. Appl. Probab

Scientific paper

Random interlacements were introduced by Sznitman in arXiv:0704.2560 and model the local picture left by simple random walk in certain graphs. This work investigates cover levels of finite sets by random interlacements, that is the least level such that the set is completely contained in the random interlacement at that level. It proves that as the cardinality of a set goes to infinity, the rescaled and recentered cover level tends in distribution to the Gumbel distribution.

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