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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Dembo, A., Sznitman, AS. On the disconnection of a discrete cylinder by a random walk. Probab. Theory Relat. Fields 136, 321–340 (2006). https://doi.org/10.1007/s00440-005-0485-9
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DOI: https://doi.org/10.1007/s00440-005-0485-9