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Blaise Pascal
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Satoshi Ishiwata
Discrete version of Dungey’s proof for the gradient heat kernel estimate on coverings
(Version discrète d’une preuve de Dungey pour les estimations du gradient du noyau de la chaleur sur les revêtements)
Annales mathématiques Blaise Pascal, 14 no. 1 (2007), p. 93-102, doi: 10.5802/ambp.229
Article PDF | Reviews Zbl 1137.60033
Class. Math.: 60J10, 58J35, 58J37
Keywords: Gradient estimates, Random walks, Gaussian estimates for the heat kernel

Résumé - Abstract

We obtain another proof of a Gaussian upper estimate for a gradient of the heat kernel on cofinite covering graphs whose covering transformation group has a polynomial volume growth. It is proved by using the temporal regularity of the discrete heat kernel obtained by Blunck [2] and Christ [3] along with the arguments of Dungey [7] on covering manifolds.


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