Electronic Journal of Probability

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

Matthew Folz

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464820231

Digital Object Identifier
doi:10.1214/EJP.v16-926

Mathematical Reviews number (MathSciNet)
MR2835251

Zentralblatt MATH identifier
1244.60099

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

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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