In this paper characterizations of graphs satisfying heat kernel estimates for a wide class of space-time scaling functions are given. The equivalence of the two-sided heat kernel estimate and the parabolic Harnack inequality is also shown via the equivalence of the upper (lower) heat kernel estimate to the parabolic mean value (and super mean value) inequality.
On the physical relevance of random walks: an example of random walks on a randomly oriented lattice
Random walk weakly attracted to a wall
Random walk in mixed random environment without uniform ellipticity
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