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Second-Order Term of Cover Time for Planar Simple Random Walk

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  • Yoshihiro Abe

    (Chiba University)

Abstract

We consider the cover time for a simple random walk on the two-dimensional discrete torus of side length n. Dembo et al. (Ann Math 160:433–464, 2004) identified the leading term in the asymptotics for the cover time as n goes to infinity. In this paper, we study the exact second order term. This is a discrete analogue of the work on the cover time for planar Brownian motion by Belius and Kistler (Probab Theory Relat Fields 167:461–552, 2017).

Suggested Citation

  • Yoshihiro Abe, 2021. "Second-Order Term of Cover Time for Planar Simple Random Walk," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1689-1747, September.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:3:d:10.1007_s10959-020-01011-2
    DOI: 10.1007/s10959-020-01011-2
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    Cited by:

    1. Collin, Orphée & Popov, Serguei, 2024. "Two-dimensional random interlacements: 0-1 law and the vacant set at criticality," Stochastic Processes and their Applications, Elsevier, vol. 169(C).

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