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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 ISSN 2052-4986.

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Official URL: http://dx.doi.org/10.1112/tlms/tlv003

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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
Divisions: Faculty of Science, Engineering and Medicine > Science > Statistics
Journal or Publication Title: Transactions of the London Mathematical Society
Publisher: London Mathematical Society
ISSN: 2052-4986
Official Date: 2015
Dates:
DateEvent
12 May 2014Submitted
5 February 2015Accepted
2015Published
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Status: Not Peer Reviewed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 (Creative Commons)
Date of first compliant deposit: 28 July 2016
Date of first compliant Open Access: 28 July 2016
Open Access Version:
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