Strict Concavity of the Half Plane Intersection Exponent for Planar Brownian Motion

Abstract

The intersection exponents for planar Brownian motion measure the exponential decay of probabilities of nonintersection of paths. We study the intersection exponent $\xi(\lambda_1,\lambda_2)$ for Brownian motion restricted to a half plane which by conformal invariance is the same as Brownian motion restricted to an infinite strip. We show that $\xi$ is a strictly concave function. This result is used in another paper to establish a universality result for conformally invariant intersection exponents.