Random walk on graphs with regular resistance and volume growth
Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 1, p. 143-169

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.

Dans cet article, nous caractérisons des graphes qui satisfont des estimées du noyau de la chaleur pour un large ensemble de fonctions d'echelles spaciaux-temporelles. L'équivalence entre l'estimée du noyau de la chaleur et l'inégalité parabolique de Harnack est également démontrée par l'équivalence de l'estimée haute (basse) du noyau de la chaleur et l'inégalité parabolique de la valeur moyenne (et de la valeur moyenne supérieure).

DOI : https://doi.org/10.1214/AIHP114
Classification:  60J10,  60J45
Keywords: random walk, heat kernel, parabolic inequalities
@article{AIHPB_2008__44_1_143_0,
     author = {Telcs, Andr\'as},
     title = {Random walk on graphs with regular resistance and volume growth},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {44},
     number = {1},
     year = {2008},
     pages = {143-169},
     doi = {10.1214/AIHP114},
     zbl = {1177.60047},
     mrnumber = {2451575},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2008__44_1_143_0}
}
Telcs, András. Random walk on graphs with regular resistance and volume growth. Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 1, pp. 143-169. doi : 10.1214/AIHP114. http://www.numdam.org/item/AIHPB_2008__44_1_143_0/

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