## Electronic Journal of Probability

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

Matthew Folz

#### 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

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

Rights