Abstract
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.
Citation
Amine Asselah. Pablo A. Ferrari. "Hitting times for independent random walks on ℤd." Ann. Probab. 34 (4) 1296 - 1338, July 2006. https://doi.org/10.1214/009117906000000106
Information