Convergence of discrete Green functions with Neumann boundary conditions

Shirshendu Ganguly, Yuval Peres

Published 2015-03-24Version 1

In this note we prove convergence of Green functions with Neumann boundary conditions for the random walk to their continuous counterparts. Also a few Beurling type hitting estimates are obtained. These have been used recently in the study of a two dimensional competing aggregation system known as $Competitive\, Erosion$. Some of the statements appearing in this note are classical for ${\mathbb{Z}}^2$. However additional arguments are needed for the proofs in the bounded geometry setting.