Electronic Journal of Probability

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

Gregory Lawler

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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.

Article information

Source
Electron. J. Probab., Volume 5 (2000), paper no. 8, 33 pp.

Dates
Accepted: 3 March 2000
First available in Project Euclid: 7 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1457376443

Digital Object Identifier
doi:10.1214/EJP.v5-64

Mathematical Reviews number (MathSciNet)
MR1768842

Zentralblatt MATH identifier
0954.60061

Subjects
Primary: 60J65: Brownian motion [See also 58J65]

Keywords
Brownian motion intersection exponent

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Lawler, Gregory. Strict Concavity of the Half Plane Intersection Exponent for Planar Brownian Motion. Electron. J. Probab. 5 (2000), paper no. 8, 33 pp. doi:10.1214/EJP.v5-64. https://projecteuclid.org/euclid.ejp/1457376443


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