The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 18, Number 4 (2008), 1441-1490.
On the disconnection of a discrete cylinder by a biased random walk
We consider a random walk on the discrete cylinder (ℤ/Nℤ)d×ℤ, d≥3 with drift N−dα in the ℤ-direction and investigate the large N-behavior of the disconnection time TNdisc, defined as the first time when the trajectory of the random walk disconnects the cylinder into two infinite components. We prove that, as long as the drift exponent α is strictly greater than 1, the asymptotic behavior of TNdisc remains N2d+o(1), as in the unbiased case considered by Dembo and Sznitman, whereas for α<1, the asymptotic behavior of TNdisc becomes exponential in N.
Ann. Appl. Probab., Volume 18, Number 4 (2008), 1441-1490.
First available in Project Euclid: 21 July 2008
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G50: Sums of independent random variables; random walks
Windisch, David. On the disconnection of a discrete cylinder by a biased random walk. Ann. Appl. Probab. 18 (2008), no. 4, 1441--1490. doi:10.1214/07-AAP491. https://projecteuclid.org/euclid.aoap/1216677128