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.
Gregory Lawler. "Strict Concavity of the Half Plane Intersection Exponent for Planar Brownian Motion." Electron. J. Probab. 5 1 - 33, 2000. https://doi.org/10.1214/EJP.v5-64