Conditioned two-dimensional simple random walk: Green's function and harmonic measure
arXiv:1907.12682 · doi:10.1007/s10959-019-00963-4
Abstract
We study the Doob's -transform of the two-dimensional simple random walk with respect to its potential kernel, which can be thought of as the two-dimensional simple random walk conditioned on never hitting the origin. We derive an explicit formula for the Green's function of this random walk, and also prove a quantitative result on the speed of convergence of the (conditional) entrance measure to the harmonic measure (for the conditioned walk) on a finite set.
23 pages, 4 figures