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Second-order term of cover time for planar simple random walk. (English) Zbl 07374950
Summary: 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).
MSC:
60G50 Sums of independent random variables; random walks
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J65 Brownian motion
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