an:05054008
Zbl 1105.60029
Dembo, Amir; Sznitman, Alain-Sol
On the disconnection of a discrete cylinder by a random walk
EN
Probab. Theory Relat. Fields 136, No. 2, 321-340 (2006).
0178-8051 1432-2064
2006
j
60G50 60D05
simple random walk; infinite discrete cylinder; disconnection time; cover time
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 \(d=1\).
Aleksander Iksanov (Kiev)