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A lower bound on the disconnection time of a discrete cylinder. (English) Zbl 1173.82360
Sidoravicius, Vladas (ed.) et al., In and out of equilibrium 2. Papers celebrating the 10th edition of the Brazilian school of probability (EBP), Rio de Janiero, Brazil, July 30 to August 4, 2006. Basel: Birkhäuser (ISBN 978-3-7643-8785-3/hbk). Progress in Probability 60, 211-227 (2008).
Summary: We study the asymptotic behavior for large \(N\) of the disconnection time \(T_N\) of simple random walk on the discrete cylinder \((\mathbb Z/N\mathbb Z)^d\times\mathbb Z\). When d is sufficiently large, we are able to substantially improve the lower bounds on \(T_N\) previously derived in [the authors, Probab. Theory Relat. Fields 136, No. 2, 321–340 (2006; Zbl 1105.60029)], for \(d\geq 2\). We show here that the laws of \(N^{2d}/T_N\) are tight.
For the entire collection see [Zbl 1141.82002].

MSC:
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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