Second order term of cover time for planar simple random walk

2017/09/24 by Yoshihiro Abe, Abe, Yoshihiro
Mathematics · Biochemistry, Genetics and Molecular Biology · #Stochastic processes and statistical mechanics #Markov Chains and Monte Carlo Methods #Diffusion and Search Dynamics

paper · pdf · doi:10.48550/arxiv.1709.08151

Abstract

We consider the cover time for a simple random walk on the two-dimensional discrete torus of side length n. Dembo, Peres, Rosen, and Zeitouni [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].

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