Strict concavity of the half plane intersection exponent for planar Brownian motion. (English) Zbl 0954.60061

Lawler, Gregory F.

Electron. J. Probab. 5, Paper No. 9, 33 p. (2000).

Summary: 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.

MSC:

60J65

Brownian motion

Keywords:

Brownian motion; intersection exponents