Duke Mathematical Journal

Sub-Gaussian estimates of heat kernels on infinite graphs

Alexander Grigor'yan and Andras Telcs

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We prove that a two-sided sub-Gaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay.

Article information

Duke Math. J., Volume 109, Number 3 (2001), 451-510.

First available in Project Euclid: 5 August 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K05: Heat equation
Secondary: 58J35: Heat and other parabolic equation methods 60G50: Sums of independent random variables; random walks 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]


Grigor'yan, Alexander; Telcs, Andras. Sub-Gaussian estimates of heat kernels on infinite graphs. Duke Math. J. 109 (2001), no. 3, 451--510. doi:10.1215/S0012-7094-01-10932-0. https://projecteuclid.org/euclid.dmj/1091737320

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