Frequently visited sets for random walks
| dc.creator | Csáki, Endre | |
| dc.creator | Földes, Antónia | |
| dc.creator | Révész, Pál | |
| dc.creator | Rosen, Jay | |
| dc.creator | Shi, Zhan | |
| dc.date | 2004-12-01 | |
| dc.date.accessioned | 2026-07-07T05:14:51Z | |
| dc.date.available | 2026-07-07T05:14:51Z | |
| dc.description | We 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.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0412018 | |
| dc.identifier | http://arxiv.org/abs/math/0412018 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73441 | |
| dc.subject | Probability | |
| dc.subject | 60G50 (primary) 60F15, 60J55 (secondary) | |
| dc.title | Frequently visited sets for random walks | |
| dc.type | text |