A Lower Bound on the Disconnection Time of a Discrete Cylinder

Details A Lower Bound on the Disconnection Time of a Discrete Cylinder A Lower Bound on the Disconnection Time of a Discrete Cylinder

2007-01-15

arxiv.org/abs/math/0701414v2

In and Out of Equilibrium 2, Progress in Probability, vol. 60, 211-227, Birkhauser, (2008)

Mathematics

Probability

17 pages, this article appears in the volume In and Out of Equilibrium 2, V. Sidoravicius and M. E. Vares Editors

Scientific paper

We study the asymptotic behavior for large N of the disconnection time T_N of simple random walk on a discrete cylinder with base a d-dimensional discrete torus of side-length N. When d is sufficiently large, we are able to substantially improve the lower bounds obtained by the authors in a previous article when d is bigger or equal to 2. We show here that the laws of N^(2d)/T_N are tight.

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