Harnack inequalities and sub-Gaussian estimates for random walks
نویسندگان
چکیده
We show that a-parabolic Harnack inequality for random walks on graphs is equivalent, on one hand, to so called-Gaussian estimates for the transition probability and, on the other hand, to the conjunction of the elliptic Harnack inequality, the doubling volume property, and the fact that the mean exit time in any ball of radius R is of the order R. The latter condition can be replaced by a certain estimate of a resistance of annuli.
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On the equivalence of parabolic Harnack inequalities and heat kernel estimates
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