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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-Peres and Ding.
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J. Jonasson and O. Schramm. On the cover time of planar graphs. Electron. Comm. Probab
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J. Kahn, J. H. Kim, L. Lovasz, and V. H. Vu. The cover time, the blanket time, and the Matthews bound. In IEEE 41 st Annual Symposium on Foundations of Computer Science (Redondo Beach, CA)
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A. Dembo, Y. Peres, J. Rosen, and O. Zeitouni. Cover times for Brownian motion and random walks in two dimensions. Annals of Mathematics
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A. Comtet, J. Desbois, and C. Texier. Functionals of Brownian motion, localization and metric graphs. Journal of Physics A
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T. Lupu. From loop clusters and random interlacement to the free field. Preprint arXiv:1402.0298
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A. S. Sznitman. Disconnection and level-set percolation for the Gaussian free field. Preprint ariv:1407.0269
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J. Ding, J. Lee, and Y. Peres. Cover times, blanket times, and majorizing measures. Annals of Mathematics
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V. Kostrykin, J. Potthoff, and R. Schrader. Brownian motion on metric graphs. J. Math. Phys
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R. Meka. A PTAS for computing the supremum of Gaussian processes. In Proceedings of the IEEE 53 rd Annual Symposium on Foundations of Computer Science (Washington, D.C.)
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J. Ding. Asymptotics of cover times via Gaussian free fields: Bounded-degree graphs and general trees. Annals of Probability
2014
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