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

Abstract

We examine the sets of late points of a symmetric random walk on $Z^2$ projected onto the torus $Z_K^2$, 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.

arXiv admin note: substantial text overlap with arXiv:1209.2383

References in corpus (4)

• Late points for random walks in two dimensions
• On the Escape of a Random Walk From Two Pieces of a Tripartite Set
• On Escaping, Entering, and Visiting Discs of Projections of Planar Symmetric Random Walks on the Lattice Torus
• Harnack Inequalities of Hitting Distributions of Projections of Planar Symmetric Random Walks on the Lattice Torus