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On the disconnection of a discrete cylinder by a random walk. (English) Zbl 1105.60029
From the authors’ summary: We investigate the large $$N$$ behaviour of the time the simple random walk on the discrete cylinder $$(Z/\mathbb{Z})^d\times \mathbb{Z}$$ needs to disconnect the discrete cylinder. We show that when $$d\geq 2$$, this time is roughly of order $$N^{2d}$$ and comparable to the cover time of the slice $$(Z/\mathbb{Z})^d\times \{0\}$$ but substantially larger than the cover time 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 $$N^{d-\varepsilon}$$. These mechanisms are in contrast with what happens when $$d=1$$.

##### MSC:
 60G50 Sums of independent random variables; random walks 60D05 Geometric probability and stochastic geometry
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##### References:
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