Affiliation:
1. CMAP, CNRS, École Polytechnique, Institut Polytechnique de Paris Palaiseau France
2. Institut für Mathematik University of Vienna Vienna Austria
Abstract
AbstractWe construct a coupling between two seemingly very different constructions of the standard additive coalescent, which describes the evolution of masses merging pairwise at rates proportional to their sums. The first construction, due to Aldous and Pitman, involves the components obtained by logging the Brownian continuum random tree (CRT) by a Poissonian rain on its skeleton as time increases. The second one, due to Bertoin, involves the excursions above its running infimum of a linear‐drifted standard Brownian excursion as its drift decreases. Our main tool is the use of an exploration algorithm of the so‐called cut‐tree of the Brownian CRT, which is a tree that encodes the genealogy of the fragmentation of the CRT.
Subject
Applied Mathematics,Computer Graphics and Computer-Aided Design,General Mathematics,Software