## Electronic Journal of Probability

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

Gregory Lawler

#### 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

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

Rights

#### 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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