Cover-time Gumbel fluctuations in finite-range, symmetric, irreducible random walks on torus
X Han,
Y Zhang,
H Ge
Abstract:In this paper, we provide the mathematical foundation for an explicit and universal feature of cover time for a large class of random work processes, which was previously observed by Chupeau et al (2015 Nat. Phys.
11 844–7). Specifically, we rigorously establish that the fluctuations of the cover time, normalized by the mean first passage time, follow a Gumbel distribution, for finite-range, symmetric, irreducible random walks on a torus of dimension three or higher. The result contributes to… Show more
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