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Probability Theory and Related Fields

, Volume 118, Issue 4, pp 455–482 | Cite as

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

  • David Aldous
  • Jim Pitman

Abstract.

Regard an element of the set of ranked discrete distributions Δ := {(x1, x2,…):x1x2≥…≥ 0, ∑ i x i = 1} as a fragmentation of unit mass into clusters of masses x i . The additive coalescent is the Δ-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 −∞ 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.

Keywords

Markov Process Unit Mass Small Cluster Discrete Distribution Random Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • David Aldous
    • 1
  • Jim Pitman
    • 1
  1. 1.Department of Statistics, University of California, 367 Evans Hall # 3860, Berkeley, CA 94720-3860, USA. e-mail: aldous@stat.berkeley.eduUS

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