Late Points and Cover Times of Projections of Planar Symmetric Random   Walks on the Lattice Torus
  We examine the sets of late points of a symmetric random walk on $Z^2$ projected onto the torus $Z^2_K$, 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. 
Michael Carlisle
math.PR