Electronic Journal of Probability

Exponential concentration of cover times

Alex Zhai

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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.

Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 32, 22 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1523325625

Digital Object Identifier
doi:10.1214/18-EJP149

Mathematical Reviews number (MathSciNet)
MR3785402

Zentralblatt MATH identifier
1391.60177

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60G60: Random fields 60G15: Gaussian processes

Keywords
random walks cover times Gaussian free fields isomorphism theorems

Rights
Creative Commons Attribution 4.0 International License.

Citation

Zhai, Alex. Exponential concentration of cover times. Electron. J. Probab. 23 (2018), paper no. 32, 22 pp. doi:10.1214/18-EJP149. https://projecteuclid.org/euclid.ejp/1523325625


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