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Department of Mathematics,
University of California San Diego

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Math 288 - Probability

Jim Pitman

UC Berkeley

The Brownian Forest

Abstract:

Harris discovered a corrrespondence 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, originallydevised by Aldous to describe the asymptotics of large finite trees, but nowrelated to the structure of a Brownian path exposed by sampling at the timesof points of an independent Poisson process.Reference: Chapter 6 of "Combinatorial Stochastic Processes", available viahttp://stat-www.berkeley.edu/users/pitman/bibliog.html

Host: Ruth Williams

February 6, 2003

9:10 AM

AP&M 6438

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