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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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