Electronic Journal of Probability

Gaussian Upper Bounds for Heat Kernels of Continuous Time Simple Random Walks

Matthew Folz

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We consider continuous time simple random walks with arbitrary speed measure $\theta$ on infinite weighted graphs. Write $p_t(x,y)$<em></em> for the heat kernel of this process. Given on-diagonal upper bounds for the heat kernel at two points $x_1,x_2$, we obtain a Gaussian upper bound for $p_t(x_1,x_2)$<em></em>. The distance function which appears in this estimate is not in general the graph metric, but a new metric which is adapted to the random walk. Long-range non-Gaussian bounds in this new metric are also established. Applications to heat kernel bounds for various models of random walks in random environments are discussed.

Article information

Electron. J. Probab., Volume 16 (2011), paper no. 62, 1693-1722.

Accepted: 12 September 2011
First available in Project Euclid: 1 June 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G50: Sums of independent random variables; random walks
Secondary: 30K08 60K37: Processes in random environments

random walk heat kernel Gaussian upper bound random walk in random environment

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Folz, Matthew. Gaussian Upper Bounds for Heat Kernels of Continuous Time Simple Random Walks. Electron. J. Probab. 16 (2011), paper no. 62, 1693--1722. doi:10.1214/EJP.v16-926. https://projecteuclid.org/euclid.ejp/1464820231

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