# Discrete version of Dungey’s proof for the gradient heat kernel estimate on coverings

Satoshi Ishiwata^{[1]}

- [1] Institute of Mathematics University of Tsukuba 1-1-1 Tennoudai, 305-8571 Ibaraki JAPAN

Annales mathématiques Blaise Pascal (2007)

- Volume: 14, Issue: 1, page 93-102
- ISSN: 1259-1734

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topIshiwata, Satoshi. "Discrete version of Dungey’s proof for the gradient heat kernel estimate on coverings." Annales mathématiques Blaise Pascal 14.1 (2007): 93-102. <http://eudml.org/doc/10543>.

@article{Ishiwata2007,

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.},

affiliation = {Institute of Mathematics University of Tsukuba 1-1-1 Tennoudai, 305-8571 Ibaraki JAPAN},

author = {Ishiwata, Satoshi},

journal = {Annales mathématiques Blaise Pascal},

keywords = {Gradient estimates; Random walks; Gaussian estimates for the heat kernel; gradient estimates; random walks},

language = {eng},

month = {1},

number = {1},

pages = {93-102},

publisher = {Annales mathématiques Blaise Pascal},

title = {Discrete version of Dungey’s proof for the gradient heat kernel estimate on coverings},

url = {http://eudml.org/doc/10543},

volume = {14},

year = {2007},

}

TY - JOUR

AU - Ishiwata, Satoshi

TI - Discrete version of Dungey’s proof for the gradient heat kernel estimate on coverings

JO - Annales mathématiques Blaise Pascal

DA - 2007/1//

PB - Annales mathématiques Blaise Pascal

VL - 14

IS - 1

SP - 93

EP - 102

AB - 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.

LA - eng

KW - Gradient estimates; Random walks; Gaussian estimates for the heat kernel; gradient estimates; random walks

UR - http://eudml.org/doc/10543

ER -

## References

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- S. Ishiwata, Asymptotic behavior of a transition probability for a random walk on a nilpotent covering graph, Contemp. Math. 347 (2004), 57-68 Zbl1061.22009MR2077030
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- E. Russ, Riesz transform on graphs for $p\>2$, unpublished manuscript

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