Discrete version of Dungey’s proof for the gradient heat kernel estimate on coverings
Annales mathématiques Blaise Pascal, Volume 14 (2007) no. 1, p. 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 : https://doi.org/10.5802/ambp.229
Classification:  60J10,  58J35,  58J37
Keywords: Gradient estimates, Random walks, Gaussian estimates for the heat kernel
@article{AMBP_2007__14_1_93_0,
     author = {Ishiwata, Satoshi},
     title = {Discrete version of Dungey's proof for the gradient heat kernel estimate on coverings},
     journal = {Annales math\'ematiques Blaise Pascal},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {14},
     number = {1},
     year = {2007},
     pages = {93-102},
     doi = {10.5802/ambp.229},
     zbl = {1137.60033},
     language = {en},
     url = {http://www.numdam.org/item/AMBP_2007__14_1_93_0}
}
Ishiwata, Satoshi . Discrete version of Dungey’s proof for the gradient heat kernel estimate on coverings. Annales mathématiques Blaise Pascal, Volume 14 (2007) no. 1, pp. 93-102. doi : 10.5802/ambp.229. http://www.numdam.org/item/AMBP_2007__14_1_93_0/

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