## The Annals of Probability

### Gaussian Estimates for Markov Chains and Random Walks on Groups

#### Abstract

A Gaussian upper bound for the iterated kernels of Markov chains is obtained under some natural conditions. This result applies in particular to simple random walks on any locally compact unimodular group $G$ which is compactly generated. Moreover, if $G$ has polynomial volume growth, the Gaussian upper bound can be complemented with a similar lower bound. Various applications are presented. In the process, we offer a new proof of Varopoulos' results relating the uniform decay of convolution powers to the volume growth of $G$.

#### Article information

Source
Ann. Probab., Volume 21, Number 2 (1993), 673-709.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176989263

Digital Object Identifier
doi:10.1214/aop/1176989263

Mathematical Reviews number (MathSciNet)
MR1217561

Zentralblatt MATH identifier
0776.60086

JSTOR