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).
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