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Late Points and Cover Times of Projections of Planar Symmetric Random Walks on the Lattice Torus (1404.3977v1)
Published 15 Apr 2014 in math.PR
Abstract: We examine the sets of late points of a symmetric random walk on $Z2$ projected onto the torus $Z2_K$, culminating in a limit theorem for the cover time of the toral random walk. This extends the work done for the simple random walk in Dembo, et al. (2006) to a large class of random walks projected onto the lattice torus. The approach uses comparisons between planar and toral hitting times and distributions on annuli, and uses only random walk methods.