Some properties of the arc sine law related to its invariance under a family of rational maps

April, 1999
Report Number: 
Jim Pitman and Marc Yor
Discrete and Computational Geometry 27: 603-634 (2002)

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.

PDF File: 
Postscript File: