Transience in growing subgraphs via evolving sets

Abstract

We extend the use of random evolving sets to time-varying conductance models and utilize it to provide tight heat kernel upper bounds. It yields the transience of any uniformly lazy random walk, on Z^d, d>=3, equipped with uniformly bounded above and below, independently time-varying edge conductances, of (effectively) non-decreasing in time vertex conductances (i.e. reversing measure), thereby affirming part of [ABGK, Conj. 7.1].