A Lower Bound on the Disconnection Time of a Discrete Cylinder

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165805We 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.17 pages, this article appears in the volume In and Out of Equilibrium 2, V. Sidoravicius and M. E. Vares EditorsProbabilityMathematical Physics60J10; 60K35; 82C41A Lower Bound on the Disconnection Time of a Discrete Cylindertext