## Harnack inequalities and sub-Gaussian estimates for random walks (2002)

by
Alexander Grigor'yan
,
Andras Telcs

Venue: | Math. Annalen |

Citations: | 30 - 6 self |

### BibTeX

@ARTICLE{Grigor'yan02harnackinequalities,

author = {Alexander Grigor'yan and Andras Telcs},

title = {Harnack inequalities and sub-Gaussian estimates for random walks},

journal = {Math. Annalen},

year = {2002},

volume = {324},

pages = {521--556}

}

### OpenURL

### Abstract

We show that a fi-parabolic Harnack inequality for random walks on graphs is equivalent, on one hand, to so called fi-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.