Gumbel fluctuations for cover times in the discrete torus

By David Belius. 2012

56 citations recorded by the source corpus.

This work proves that the fluctuations of the cover time of simple random walk in the discrete torus of dimension at least three with large side-length are governed by the Gumbel extreme value distribution. This result was conjectured for example in Aldous and Fill (Reversible Markov chains and random walks on graphs, in preparation). We also derive some corollaries which qualitatively describe “how” covering happens. In addition, we develop a new and stronger coupling of the model of random interlacements, introduced by Sznitman (Ann Math (2) 171(3):2039–2087, 2010), and random walk in the torus. This coupling is used to prove the cover time result and is also of independent interest.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d27961064a4f133e94695b40c2cbbe25d8745278

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In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Soft local times and decoupling of random interlacements (2012, background): “Recent works have also shown a connection between: random interlacements, the Gaussian free field [19], [27] and cover times of random walks [2].”
The subleading order of two dimensional cover times (2014, background): “The above can be constrasted with the situation for discrete torii of higher dimensions, about which much more is known, see [4, 17].”