On the disconnection of a discrete cylinder by a random walk |
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Authors: | Amir Dembo Alain-Sol Sznitman |
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Institution: | (1) Department of Mathematics and Department of Statistics, Stanford University, Stanford, CA 94305, USA;(2) Departement Mathematik, ETH-Zentrum, 8092 Zürich, Switzerland |
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Abstract: | We investigate the large N behavior of the time the simple random walk on the discrete cylinder
needs to disconnect the discrete cylinder. We show that when d≥2, this time is roughly of order N
2
d
and comparable to the cover time of the slice
, but substantially larger than the cover timer of the base by the projection of the walk. Further we show that by the time
disconnection occurs, a massive ``clogging' typically takes place in the truncated cylinders of height
. These mechanisms are in contrast with what happens when d=1. |
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Keywords: | |
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