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March 2014 Asymptotics of cover times via Gaussian free fields: Bounded-degree graphs and general trees
Jian Ding
Ann. Probab. 42(2): 464-496 (March 2014). DOI: 10.1214/12-AOP822

Abstract

In this paper we show that on bounded degree graphs and general trees, the cover time of the simple random walk is asymptotically equal to the product of the number of edges and the square of the expected supremum of the Gaussian free field on the graph, assuming that the maximal hitting time is significantly smaller than the cover time. Previously, this was only proved for regular trees and the 2D lattice. Furthermore, for general trees, we derive exponential concentration for the cover time, which implies that the standard deviation of the cover time is bounded by the geometric mean of the cover time and the maximal hitting time.

Citation

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Jian Ding. "Asymptotics of cover times via Gaussian free fields: Bounded-degree graphs and general trees." Ann. Probab. 42 (2) 464 - 496, March 2014. https://doi.org/10.1214/12-AOP822

Information

Published: March 2014
First available in Project Euclid: 24 February 2014

zbMATH: 1316.60064
MathSciNet: MR3178464
Digital Object Identifier: 10.1214/12-AOP822

Subjects:
Primary: 60G15, 60G60, 60J10

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 2 • March 2014
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