Electronic Journal of Probability

Exponential concentration of cover times

Alex Zhai

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

random walks cover times Gaussian free fields isomorphism theorems

Creative Commons Attribution 4.0 International License.


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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