Exponential concentration of cover times

Alex Zhai

doi:10.1214/18-EJP149

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Home > Journals > Electron. J. Probab. > Volume 23 > Article

2018 Exponential concentration of cover times

Alex Zhai

Electron. J. Probab. 23: 1-22 (2018). DOI: 10.1214/18-EJP149

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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.