Hitting times for independent random walks on $\mathbb{Z}^d$

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dc.creatorAsselah, Amine
dc.creatorFerrari, Pablo A.
dc.date2004-03-22
dc.date2006-09-21
dc.date.accessioned2026-07-07T06:36:03Z
dc.date.available2026-07-07T06:36:03Z
dc.descriptionWe consider a system of asymmetric independent random walks on $\mathbb{Z}^d$, denoted by $\{η_t,t\in{\mathbb{R}}\}$, stationary under the product Poisson measure $ν_ρ$ of marginal density $ρ>0$. We fix a pattern $\mathcal{A}$, an increasing local event, and denote by $τ$ the hitting time of $\mathcal{A}$. By using a loss network representation of our system, at small density, we obtain a coupling between the laws of $η_t$ conditioned on $\{τ>t\}$ for all times $t$. When $d\ge3$, this provides bounds on the rate of convergence of the law of $η_t$ conditioned on $\{τ>t\}$ toward its limiting probability measure as $t$ tends to infinity. We also treat the case where the initial measure is close to $ν_ρ$ without being product.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117906000000106 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0403351
dc.identifierhttp://arxiv.org/abs/math/0403351
dc.identifierAnnals of Probability 2006, Vol. 34, No. 4, 1296-1338
dc.identifierdoi:10.1214/009117906000000106
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99969
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35, 82C22, 60J25 (Primary)
dc.titleHitting times for independent random walks on $\mathbb{Z}^d$
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