Strict Concavity of the Half Plane Intersection Exponent for Planar Brownian Motion
Gregory F. Lawler, Duke University and Cornell University
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.
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