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2018 Exponential concentration of cover times
Alex Zhai
Electron. J. Probab. 23: 1-22 (2018). DOI: 10.1214/18-EJP149

Abstract

We prove an exponential concentration bound for cover times of general graphs in terms of the Gaussian free field, extending the work of Ding, Lee, and Peres [8] and Ding [7]. The estimate is asymptotically sharp as the ratio of hitting time to cover time goes to zero.

The bounds are obtained by showing a stochastic domination in the generalized second Ray-Knight theorem, which was shown to imply exponential concentration of cover times by Ding in [7]. This stochastic domination result appeared earlier in a preprint of Lupu [22], but the connection to cover times was not mentioned.

Citation

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Alex Zhai. "Exponential concentration of cover times." Electron. J. Probab. 23 1 - 22, 2018. https://doi.org/10.1214/18-EJP149

Information

Received: 21 February 2017; Accepted: 8 February 2018; Published: 2018
First available in Project Euclid: 10 April 2018

zbMATH: 1391.60177
MathSciNet: MR3785402
Digital Object Identifier: 10.1214/18-EJP149

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

JOURNAL ARTICLE
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