Annals of Probability

Hitting times for special patterns in the symmetric exclusion process on ℤd

Amine Asselah and Paolo Dai Pra

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Abstract

We consider the symmetric exclusion process {ηt,t>0} on {0,1}d. We fix a pattern ${\mathcal{A}}:=\{\eta: \sum_{\Lambda}\eta(i)\ge k\}$, where Λ is a finite subset of ℤd and k is an integer, and we consider the problem of establishing sharp estimates for τ, the hitting time of ${\mathcal{A}}$. We present a novel argument based on monotonicity which helps in some cases to obtain sharp tail asymptotics for τ in a simple way. Also, we characterize the trajectories {ηs,st} conditioned on {τ>t}.

Article information

Source
Ann. Probab., Volume 32, Number 4 (2004), 3301-3323.

Dates
First available in Project Euclid: 8 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aop/1107883354

Digital Object Identifier
doi:10.1214/009117904000000487

Mathematical Reviews number (MathSciNet)
MR2094446

Zentralblatt MATH identifier
1067.60096

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C22: Interacting particle systems [See also 60K35] 60J25: Continuous-time Markov processes on general state spaces

Keywords
Quasistationary measures attractive processes hitting times Yaglom limit h process

Citation

Asselah, Amine; Pra, Paolo Dai. Hitting times for special patterns in the symmetric exclusion process on ℤ d. Ann. Probab. 32 (2004), no. 4, 3301--3323. doi:10.1214/009117904000000487. https://projecteuclid.org/euclid.aop/1107883354


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