Cover levels and random interlacements

Abstract

This note investigates cover levels of finite sets in the random interlacements model introduced in [Ann. of Math. (2) 171 (2010) 2039-2087], 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 with cumulative distribution function $\exp (-\exp (-z))$.

Published in at http://dx.doi.org/10.1214/11-AAP770 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• On the fragmentation of a torus by random walk
• Uniformity of the uncovered set of random walk and cutoff for lamplighter chains
• Upper bound on the disconnection time of discrete cylinders and random interlacements

Cited by in corpus (2)

• Random interlacements and amenability
• An improved decoupling inequality for random interlacements