Translator Disclaimer
2011 Gaussian Upper Bounds for Heat Kernels of Continuous Time Simple Random Walks
Matthew Folz
Author Affiliations +
Electron. J. Probab. 16: 1693-1722 (2011). DOI: 10.1214/EJP.v16-926

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.

Citation

Download Citation

Matthew Folz. "Gaussian Upper Bounds for Heat Kernels of Continuous Time Simple Random Walks." Electron. J. Probab. 16 1693 - 1722, 2011. https://doi.org/10.1214/EJP.v16-926

Information

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

zbMATH: 1244.60099
MathSciNet: MR2835251
Digital Object Identifier: 10.1214/EJP.v16-926

Subjects:
Primary: 60G50
Secondary: 30K08, 60K37

JOURNAL ARTICLE
30 PAGES


SHARE
Vol.16 • 2011
Back to Top