On Escaping, Entering, and Visiting Discs of Projections of Planar Symmetric Random Walks on the Lattice Torus

Abstract

We examine escape and entrance times, Green's functions, local times, and hitting distributions of discs and annuli of a symmetric random walk on ${\mathbb{Z}}^2$ projected onto the periodic lattice ${\mathbb{Z}}_K^2$. This extends a framework for the simple planar random walk in Dembo, et al. (2006) to the large class of planar random walks in Bass, Rosen (2007). The approach uses comparisons between ${\mathbb{Z}}^2$ and ${\mathbb{Z}}_K^2$ hitting times and distributions on annuli, and uses only random walk methods.

31 pages, 4 figures

References in corpus (2)

• Late points for random walks in two dimensions
• On the Escape of a Random Walk From Two Pieces of a Tripartite Set

Cited by in corpus (2)

• Harnack Inequalities of Hitting Distributions of Projections of Planar Symmetric Random Walks on the Lattice Torus
• Late Points and Cover Times of Projections of Planar Symmetric Random Walks on the Lattice Torus