  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.
