Medallion Lecture: The disconnection time of the random walk on a discrete cylinder

Friday, August 5, 2005 - 4:45pm - 6:00pm
EE/CS 3-180
Amir Dembo (Stanford University)
Consider the simple random walk on the discrete cylinder whose base is the d-dimnesional torus with side-length N, and whose height is the set of all integers. When d>1, the time the walk needs to disconnect the discrete cylinder is very roughly of order N to the power 2d, and comparable to the cover time of the slice of height 0. Further, by the time disconnection occurs, a massive clogging takes place in the truncated cylinders of height N to power d' for any d'
I shall also describe what we know about the disconnection time for base graphs other than the d-dimensional torus.

This talk is based on a joint work with Alain-Sol Sznitman.