Open Access
2015 Maximum and minimum of local times for two-dimensional random walk
Yoshihiro Abe
Author Affiliations +
Electron. Commun. Probab. 20: 1-14 (2015). DOI: 10.1214/ECP.v20-3877


We obtain the leading orders of the maximum and the minimum of local times for the simple random walk on the two-dimensional torus at time proportional to the cover time. We also estimate the number of points with large (or small) values of the local times. These are analogues of estimates on the two-dimensional Gaussian free fields by Bolthausen, Deuschel, and Giacomin [Ann. Probab., 29 (2001)] and Daviaud [Ann. Probab., 34 (2006)], but we have different exponents from the case of the Gaussian free field.


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Yoshihiro Abe. "Maximum and minimum of local times for two-dimensional random walk." Electron. Commun. Probab. 20 1 - 14, 2015.


Accepted: 5 March 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1321.60151
MathSciNet: MR3320410
Digital Object Identifier: 10.1214/ECP.v20-3877

Primary: 60J55
Secondary: 60G70 , 60J10

Keywords: Gaussian free fields , Local times , Two-dimensional random walks

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