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Moduli of continuity of local times of random walks on graphs in terms of the resistance metric
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Croydon, David A. (2015) Moduli of continuity of local times of random walks on graphs in terms of the resistance metric. Transactions of the London Mathematical Society, Volume 2 (Number 1). pp. 57-79. doi: 10.1112/tlms/tlv003
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Official URL: http://dx.doi.org/10.1112/tlms/tlv003
Abstract
In this article, universal concentration estimates are established for the local times of random walks on weighted graphs in terms of the resistance metric. As a particular application of these, a modulus of continuity for local times is provided in the case when the graphs in question satisfy a certain volume growth condition with respect to the resistance metric. Moreover, it is explained how these results can be applied to self-similar fractals, for which they are shown to be useful for deriving scaling limits for local times and asymptotic bounds for the cover time distribution.
| Item Type: | Journal Article | ||||||||
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| Divisions: | Faculty of Science > Statistics | ||||||||
| Journal or Publication Title: | Transactions of the London Mathematical Society | ||||||||
| Publisher: | London Mathematical Society | ||||||||
| ISSN: | 2052-4986 | ||||||||
| Official Date: | 2015 | ||||||||
| Dates: |
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| Volume: | Volume 2 | ||||||||
| Number: | Number 1 | ||||||||
| Page Range: | pp. 57-79 | ||||||||
| DOI: | 10.1112/tlms/tlv003 | ||||||||
| Status: | Not Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access | ||||||||
| Open Access Version: |
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