Abstract
Moderate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed in a geometric point of view. They deal with any intermediate spatial scalings between those of laws of large numbers and those of central limit theorems. The corresponding rate functions are given by quadratic forms determined by the Albanese metric associated with the given random walks. We apply MDPs to establish laws of the iterated logarithm on the covering graphs by characterizing the set of all limit points of the normalized random walks.
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 18J10225
Award Identifier / Grant number: 19K23410
Funding statement: The author is supported by Grant-in-Aid for JSPS Fellows No. 18J10225 and Grant-in-Aid for Research Activity start-up No. 19K23410.
Acknowledgements
The author would like to thank the anonymous referee for his or her helpful suggestions which make the present paper more readable.
Communicated by: Maria Gordina
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