Conditioned two-dimensional simple random walk: Green's function and harmonic measure
Probability
2021-04-27 v2
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.
Cite
@article{arxiv.1907.12682,
title = {Conditioned two-dimensional simple random walk: Green's function and harmonic measure},
author = {Serguei Popov},
journal= {arXiv preprint arXiv:1907.12682},
year = {2021}
}
Comments
23 pages, 4 figures