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]
Ishiwata, Satoshi1
1 Institute of Mathematics University of Tsukuba 1-1-1 Tennoudai, 305-8571 Ibaraki JAPAN
Annales mathématiques Blaise Pascal, Tome 14 (2007) no. 1, pp. 93-102.

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.

DOI : 10.5802/ambp.229
Classification : 60J10, 58J35, 58J37
Mots-clés : Gradient estimates, Random walks, Gaussian estimates for the heat kernel
Ishiwata, Satoshi 1

1 Institute of Mathematics University of Tsukuba 1-1-1 Tennoudai, 305-8571 Ibaraki JAPAN 
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Ishiwata, Satoshi. Discrete version of Dungey’s proof for the gradient heat kernel estimate on coverings. Annales mathématiques Blaise Pascal, Tome 14 (2007) no. 1, pp. 93-102. doi : 10.5802/ambp.229. http://www.numdam.org/articles/10.5802/ambp.229/

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