Open Access
July 2006 Hitting times for independent random walks on ℤd
Amine Asselah, Pablo A. Ferrari
Ann. Probab. 34(4): 1296-1338 (July 2006). DOI: 10.1214/009117906000000106


We consider a system of asymmetric independent random walks on ℤd, denoted by {ηt,t∈ℝ}, stationary under the product Poisson measure νρ 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 ηt conditioned on {τ>t} for all times t. When d≥3, this provides bounds on the rate of convergence of the law of ηt 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 νρ without being product.


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Amine Asselah. Pablo A. Ferrari. "Hitting times for independent random walks on ℤd." Ann. Probab. 34 (4) 1296 - 1338, July 2006.


Published: July 2006
First available in Project Euclid: 19 September 2006

zbMATH: 1101.60074
MathSciNet: MR2257648
Digital Object Identifier: 10.1214/009117906000000106

Primary: 60J25 , 60K35 , 82C22

Keywords: Birkhoff–Hopf , hitting time , Loss network , Particle system

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 4 • July 2006
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