Title: Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent
Author: David Aldous and Jim Pitman
Date: October 1998
Abstract:
Regard an element of the set of ranked discrete distributions
$\Delta := \{(x_1,x_2,\ldots): x_1 \geq x_2 \geq \ldots \geq 0, \sum_i x_i = 1\}$
as a fragmentation of unit mass into clusters of masses $x_i$. The
additive coalescent is the $\Delta$-valued Markov process in which
pairs of clusters of masses $\{x_i,x_j\}$ merge
into a cluster of mass $x_i + x_j$ at rate $x_i+x_j$.
Aldous and Pitman (1998) showed that a version of this process
starting from time $-\infty$ with infinitesimally small clusters
can be constructed from the Brownian continuum random tree of
Aldous (1991,1993) by Poisson splitting along the skeleton of the tree.
In this paper it is shown that the general such process may be
constructed analogously from a new family of inhomogeneous
continuum random trees.