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hal-00011249, version 1

## Hitting times for independent random walks

Amine Asselah 1, Pablo A. Ferrari

(2004)

Abstract: We consider a system of asymmetric independent random walks on $Z^d$, denoted by $\{\eta_t,t\in R\}$, stationary under the product Poisson measure $\nu_{\rho}$ of marginal density $\rho>0$. We fix a pattern $A$, an increasing local event, and denote by $\tau$ the hitting time of $A$. By using a Loss Network representation of our system, at small density, we obtain a coupling between the laws of $\eta_t$ conditioned on $\{\tau>t\}$ for all times $t$. When $d\ge 3$, this provides bounds on the rate of convergence of the law of $\eta_t$ conditioned on $\{\tau>t\}$ towards its limiting probability measure as $t$ tends to infinity. We also treat the case where the initial measure is {\it close} to $\nu_{\rho}$ without being product.

• 1:  Laboratoire d'Analyse, Topologie, Probabilités (LATP)
• CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III
• Domain : Mathematics/Probability
Mathematics/Mathematical Physics
Physics/Mathematical Physics
• Comment : 35 pages

• hal-00011249, version 1
• oai:hal.archives-ouvertes.fr:hal-00011249
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• Submitted on: Thursday, 13 October 2005 22:59:31
• Updated on: Thursday, 13 October 2005 22:59:31