The Annals of Probability

Upper bound on the disconnection time of discrete cylinders and random interlacements

Alain-Sol Sznitman

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Abstract

We study the asymptotic behavior for large N of the disconnection time TN of a simple random walk on the discrete cylinder (ℤ/Nℤ)d×ℤ, when d≥2. We explore its connection with the model of random interlacements on ℤd+1 recently introduced in [Ann. Math., in press], and specifically with the percolative properties of the vacant set left by random interlacements. As an application we show that in the large N limit the tail of TN/N2d is dominated by the tail of the first time when the supremum over the space variable of the Brownian local times reaches a certain critical value. As a by-product, we prove the tightness of the laws of TN/N2d, when d≥2.

Article information

Source
Ann. Probab., Volume 37, Number 5 (2009), 1715-1746.

Dates
First available in Project Euclid: 21 September 2009

Permanent link to this document
https://projecteuclid.org/euclid.aop/1253539855

Digital Object Identifier
doi:10.1214/09-AOP450

Mathematical Reviews number (MathSciNet)
MR2561432

Zentralblatt MATH identifier
1179.60025

Subjects
Primary: 60G50: Sums of independent random variables; random walks 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]

Keywords
Disconnection random walks random interlacements discrete cylinders

Citation

Sznitman, Alain-Sol. Upper bound on the disconnection time of discrete cylinders and random interlacements. Ann. Probab. 37 (2009), no. 5, 1715--1746. doi:10.1214/09-AOP450. https://projecteuclid.org/euclid.aop/1253539855


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References

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