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  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 in . This stochastic domination result appeared earlier in a preprint of Lupu , but the connection to cover times was not mentioned.
"Exponential concentration of cover times." Electron. J. Probab. 23 1 - 22, 2018. https://doi.org/10.1214/18-EJP149