We prove equivalent conditions for two-sided sub-Gaussian estimates of heat
kernels on metric measure spaces.Comment: Published in at http://dx.doi.org/10.1214/11-AOP645 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
We prove that a two-sided sub-Gaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay.
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