TL;DR
This paper establishes an exponential concentration bound for cover times in general graphs using the Gaussian free field, extending previous work and providing asymptotic sharpness as certain ratios tend to zero.
Contribution
It introduces a stochastic domination approach in the generalized second Ray-Knight theorem to derive exponential concentration bounds for cover times, linking it to Gaussian free fields.
Findings
Proves exponential concentration bounds for cover times.
Extends previous work by Ding-Lee-Peres and Ding.
Shows asymptotic sharpness of the bounds.
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-Peres and Ding. 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. This stochastic domination result appeared earlier in a preprint of Lupu, but the connection to cover times was not mentioned.
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