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VOL. 45 | 2004 Some properties of the arc-sine law related to its invariance under a family of rational maps

Abstract

This paper shows how the invariance of the arc-sine distribution on (0, 1) under a family of rational maps is related on the one hand to various integral identities with probabilistic interpretations involving random variables derived from Brownian motion with arc-sine, Gaussian, Cauchy and other distributions, and on the other hand to results in the analytic theory of iterated rational maps.

Information

Published: 1 January 2004
First available in Project Euclid: 28 November 2007

zbMATH: 1268.37071
MathSciNet: MR2126891

Digital Object Identifier: 10.1214/lnms/1196285384

Subjects:
Primary: 58F11
Secondary: 30D05 , 31A15 , 60J65

Keywords: Brownian motion , Cauchy distribution , conformal invariance , harmonic measure , inner function , invariant measure

Rights: Copyright © 2004, Institute of Mathematical Statistics

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Vol. 45 • 1 January 2004
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