Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent

• 成果类型: Article
• 署名作者: Aldous, D; Pitman, J
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/PL00008751
• 发表日期: 2000
• 页码: 455-482
• 关键词: coagulation; models

摘要

Regard an element of the set of ranked discrete distributions Delta := {(x(1), x(2),...) : x(1) greater than or equal to x(2) greater than or equal to ... greater than or equal to 0, Sigma (i) x(i) = 1} as a fragmentation of unit mass into clusters of masses xi. 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 -infinity 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.