We study discrete time random walks in an environment of i.i.d. non-negative bounded conductances in $\mathbb{Z}^d$. We are interested in the anomaly of the heat kernel decay. We improve recent results and techniques.
Comparison of quenched and annealed invariance principles for random conductance model: Part II
Isoperimetry and heat kernel decay on percolation clusters
Harnack inequalities on weighted graphs and some applications to the random conductance model
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