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Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent
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  • Published: December 2000

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

  • David Aldous1 &
  • Jim Pitman1 

Probability Theory and Related Fields volume 118, pages 455–482 (2000)Cite this article

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  • 38 Citations

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Abstract.

Regard an element of the set of ranked discrete distributions Δ := {(x 1, x 2,…):x 1≥x 2≥…≥ 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.

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Authors and Affiliations

  1. Department of Statistics, University of California, 367 Evans Hall # 3860, Berkeley, CA 94720-3860, USA. e-mail: aldous@stat.berkeley.edu, , , , , , US

    David Aldous & Jim Pitman

Authors
  1. David Aldous
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  2. Jim Pitman
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Received: 6 October 1998 / Revised version: 16 May 1999 / Published online: 20 October 2000

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Aldous, D., Pitman, J. Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent. Probab Theory Relat Fields 118, 455–482 (2000). https://doi.org/10.1007/PL00008751

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  • Issue Date: December 2000

  • DOI: https://doi.org/10.1007/PL00008751

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Keywords

  • Markov Process
  • Unit Mass
  • Small Cluster
  • Discrete Distribution
  • Random Tree
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