Anomalous heat kernel behaviour for the dynamic random conductance model

Abstract

We introduce the time dynamic random conductance model and consider the heat kernel for the random walk on this environment. In the case where conductances are bounded above, an example environment is presented which exhibits heat kernel decay that is asymptotically slower than in the well studied time homogeneous case - being close to $O\left( n^{-1}\right) $ as opposed to $O\left( n^{-2}\right) $. The example environment given is a modification of an environment introduced in Berger, Biskup, Hoffman and Kozma (2008).