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.
Keywords: Gradient estimates, Random walks, Gaussian estimates for the heat kernel
Satoshi Ishiwata 1
@article{AMBP_2007__14_1_93_0, author = {Satoshi Ishiwata}, title = {Discrete version of {Dungey{\textquoteright}s} proof for the gradient heat kernel estimate on coverings}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {93--102}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {14}, number = {1}, year = {2007}, doi = {10.5802/ambp.229}, zbl = {1137.60033}, language = {en}, url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.229/} }
TY - JOUR AU - Satoshi Ishiwata TI - Discrete version of Dungey’s proof for the gradient heat kernel estimate on coverings JO - Annales mathématiques Blaise Pascal PY - 2007 SP - 93 EP - 102 VL - 14 IS - 1 PB - Annales mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.229/ DO - 10.5802/ambp.229 LA - en ID - AMBP_2007__14_1_93_0 ER -
%0 Journal Article %A Satoshi Ishiwata %T Discrete version of Dungey’s proof for the gradient heat kernel estimate on coverings %J Annales mathématiques Blaise Pascal %D 2007 %P 93-102 %V 14 %N 1 %I Annales mathématiques Blaise Pascal %U https://ambp.centre-mersenne.org/articles/10.5802/ambp.229/ %R 10.5802/ambp.229 %G en %F AMBP_2007__14_1_93_0
Satoshi Ishiwata. 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. https://ambp.centre-mersenne.org/articles/10.5802/ambp.229/
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