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 Electronic Journal of Probability > Vol. 5 (2000) > Paper 8 open journal systems 


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.


Full text: PDF

Pages: 1-33

Published on: March 3, 2000
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Electronic Journal of Probability. ISSN: 1083-6489