Late Points and Cover Times of Projections of Planar Symmetric Random Walks on the Lattice Torus

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We examine the sets of late points of a symmetric random walk on Z² projected onto the torus Z²ₖ, 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.