Abstract #302111

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JSM 2003 Abstract #302111
Activity Number: 8
Type: Invited
Date/Time: Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #302111
Title: A System of Interacting Rayleigh Processes Related to the Brownian Tree
Author(s): Jim Pitman*+
Companies: University of California, Berkeley
Address: Dept. Statistics, Berkeley, CA, 94720-3860,
Keywords: Rayleigh ; process ; Brownian ; tree
Abstract:

Harris discovered a correspondence between random walk excursions and random trees whose continuous analog relates a Brownian excursion to Aldous's concept of a continuum random tree. This idea has been developed and applied in various ways by Neveu, Le Gall, and others. I will review these ideas in terms of a forest growth process, originally devised by Aldous to describe the asymptotics of large finite trees, but now related to the structure of a Brownian path exposed by sampling at the times of points of an independent Poisson process. As an application of these ideas, I describe an infinite system of interacting Rayleigh processes related to Aldous's construction of the tree in a Brownian excursion and the asymptotic behavior for large n of the Aldous-Broder algorithm for generating a uniform random tree with n vertices.

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