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- Publisher
- de Gruyter
- Copyright
- © 2020 Walter de Gruyter GmbH, Berlin/Boston
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- DOI
- 10.1515/forum-2020-0070
- Publisher site
- See Article on Publisher Site
Abstract
AbstractModerate 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.
Journal
Forum Mathematicum – de Gruyter
Published: Jan 1, 2021