Harnack Inequalities of Hitting Distributions of Projections of Planar Symmetric Random Walks on the Lattice Torus

Abstract

We give Harnack inequalities for the hitting distributions of a large family of symmetric random walks on ${\mathbb{Z}}^2$, and their projections onto the lattice torus ${\mathbb{Z}}_K^2$. This extends a framework for the simple random walk in Dembo, et al. (2006), and generalizes the results in Bass, Rosen (2007) to the toral projection.

21 pages, 1 figure

References in corpus (3)

• 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

Cited by in corpus (1)

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