A boundary Harnack principle and its application to analyticity of 3D Brownian intersection exponents

Abstract

We show that a domain in ${\mathbb{R}}^3$ with the trace of a 3D Brownian motion removed almost surely satisfies the boundary Harnack principle (BHP). Then, we use it to prove that the intersection exponents for 3D Brownian motion are analytic.

49 pages, 5 figures