The Einstein relation for random walks on graphs

Details The Einstein relation for random walks on graphs The Einstein relation for random walks on graphs

2008-01-15

arxiv.org/abs/0801.2336v1

Journal of Statistical Physics, 122, 4, 2006, 617-645

Mathematics

Probability

Scientific paper

This paper investigates the Einstein relation; the connection between the volume growth, the resistance growth and the expected time a random walk needs to leave a ball on a weighted graph. The Einstein relation is proved under different set of conditions. In the simplest case it is shown under the volume doubling and time comparison principles. This and the other set of conditions provide the basic framework for the study of (sub-) diffusive behavior of the random walks on weighted graphs.

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