On the Disconnection of a Discrete Cylinder by a Biased Random Walk by David Windisch
نویسنده
چکیده
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 T disc N , 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 T disc N remains N 2d+o(1), as in the unbiased case considered by Dembo and Sznitman, whereas for α < 1, the asymptotic behavior of T disc N becomes exponential in N .
منابع مشابه
On the Disconnection of a Discrete Cylinder by a Biased Random Walk
We consider a random walk on the discrete cylinder (Z/NZ)×Z, d ≥ 3 with drift N in the Z-direction and investigate the large N -behavior of the disconnection time T disc N , 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 T...
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