Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent
Regard an element of the set of ranked discrete distributions \(\Delta:=\{(x_1,x_2,\dots):x_1\geq x_2\geq \ldots \geq 0\), \(\sum_i x_i=1\}\) 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 \(x_i+x_j\). It has been shown in previous papers that a version of this process starting from time \(-\infty\) with infinitesimally small clusters can be constructed from the Brownian continuum random tree by Poisson splitting along a 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.
scientific article; zbMATH DE number 1563072