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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 44 open journal systems 


The mass of sites visited by a random walk on an infinite graph

Lee R Gibson, University of Louisville


Abstract
We determine the log-asymptotic decay rate of the negative exponential moments of the mass of sites visited by a random walk on an infinite graph which satisfies a two-sided sub-Gaussian estimate on its transition kernel. This provides a new method of proof of the correct decay rate for Cayley graphs of finitely generated groups with polynomial volume growth. This method also extend known results by determining this decay rate for certain graphs with fractal-like structure or with non-Alfors regular volume growth functions.


Full text: PDF

Pages: 1257-1282

Published on: August 4, 2008
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Electronic Journal of Probability. ISSN: 1083-6489