Translator Disclaimer
2008 A special set of exceptional times for dynamical random walk on $Z^2$
Gideon Amir, Christopher Hoffman
Author Affiliations +
Electron. J. Probab. 13: 1927-1951 (2008). DOI: 10.1214/EJP.v13-571

Abstract

In [2] Benjamini, Haggstrom, Peres and Steif introduced the model of dynamical random walk on the $d$-dimensional lattice $Z^d$. This is a continuum of random walks indexed by a time parameter $t$. They proved that for dimensions $d=3,4$ there almost surely exist times $t$ such that the random walk at time $t$ visits the origin infinitely often, but for dimension 5 and up there almost surely do not exist such $t$. Hoffman showed that for dimension 2 there almost surely exists $t$ such that the random walk at time $t$ visits the origin only finitely many times [5]. We refine the results of [5] for dynamical random walk on $Z^2$, showing that with probability one the are times when the origin is visited only a finite number of times while other points are visited infinitely often.

Citation

Download Citation

Gideon Amir. Christopher Hoffman. "A special set of exceptional times for dynamical random walk on $Z^2$." Electron. J. Probab. 13 1927 - 1951, 2008. https://doi.org/10.1214/EJP.v13-571

Information

Accepted: 30 October 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1190.60034
MathSciNet: MR2453551
Digital Object Identifier: 10.1214/EJP.v13-571

Subjects:
Primary: 60G50
Secondary: 82C41

JOURNAL ARTICLE
25 PAGES


SHARE
Vol.13 • 2008
Back to Top