Upper escape rate of Markov chains on weighted graphs

Xueping Huang, Yuichi Shiozawa

Published 2013-04-23Version 1

We obtain an upper escape rate function for a continuous time minimal symmetric Markov chain, defined on a locally finite weighted graph. This upper rate function is given in terms of volume growth with respect to an adapted path metric and has the same form as the manifold setting. Our approach also gives a slightly more restrictive form of Folz's theorem on conservativeness as a consequence.