On the disconnection of a discrete cylinder by a random walk.

We investigate the large N behavior of the time the simple random walk on the discrete cylinder [InlineMediaObject not available: see fulltext.] 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 [InlineMediaObject not available: see fulltext.], 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 [InlineMediaObject not available: see fulltext.]. These mechanisms are in contrast with what happens when d=1. [ABSTRACT FROM AUTHOR]