Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent
type: Item
instance of: scholarly article
title: Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent
zbMATH Open document ID: 0969.60015
publication date: 2001-09-23T00:00:00Z
review text: 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.
reviewed by: Klaus Dohmen
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60J50
zbMATH DE Number: 1563072
zbMATH Keywords: random tree
zbMATH Keywords: entrance boundary
zbMATH Keywords: coalescent
author: David Aldous
author: Jim Pitman
MaRDI profile type: Publication
DOI: 10.1007/S004400000094
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1563072