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
