Two-sided random walks conditioned to have no intersections

Abstract

Let $S^1,S^2$ be independent simple random walks in ${\mathbb{Z}}^d$ ($d=2,3$) started at the origin. We construct two-sided random walk paths conditioned that $S^1[0,\infty )\cap S^2[1,\infty )=\varnothing$.

arXiv comment25 pages