Jim Pitman, University of California, Berkeley

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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, 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.

Reference: Chapter 6 of "Combinatorial Stochastic Processes", available by clicking here.