Analyticity of intersection exponents for planar Brownian motion

The goal of the present paper is to show that the intersection exponents for planar Brownian motions are analytic. Let k~>l be a positive integer and let X 1 , . . . , X k be independent Brownian motions in the complex plane C started from 0. Let Y, y1, y2, ... denote other independent planar Brownian motions started from 1, and let St be the random variable (measurable with respect to X 1, ..., X k)