Frequently visited sets for random walks

dc.creatorCsáki, Endre
dc.creatorFöldes, Antónia
dc.creatorRévész, Pál
dc.creatorRosen, Jay
dc.creatorShi, Zhan
dc.date2004-12-01
dc.date.accessioned2026-07-07T05:14:51Z
dc.date.available2026-07-07T05:14:51Z
dc.descriptionWe study the occupation measure of various sets for a symmetric transient random walk in $Z^d$ with finite variances. Let $μ^X_n(A)$ denote the occupation time of the set $A$ up to time $n$. It is shown that $\sup_{x\in Z^d}μ_n^X(x+A)/\log n$ tends to a finite limit as $n\to\infty$. The limit is expressed in terms of the largest eigenvalue of a matrix involving the Green's function of $X$ restricted to the set $A$. Some examples are discussed and the connection to similar results for Brownian motion is given.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/math/0412018
dc.identifierhttp://arxiv.org/abs/math/0412018
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73441
dc.subjectProbability
dc.subject60G50 (primary) 60F15, 60J55 (secondary)
dc.titleFrequently visited sets for random walks
dc.typetext

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