The mass of sites visited by a random walk on an infinite graph. (English) Zbl 1191.60059
Summary: 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.
MSC:
60G50 | Sums of independent random variables; random walks |
60J05 | Discrete-time Markov processes on general state spaces |
60K37 | Processes in random environments |