The standard additive coalescent

@article{Aldous1998TheSA,
  title={The standard additive coalescent},
  author={David J. Aldous and Jim Pitman},
  journal={Annals of Probability},
  year={1998},
  volume={26},
  pages={1703-1726}
}
Regard an element of the set 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 of Evans and Pitman 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 . They showed that a version (X ∞ (t), -∞ < t < ∞) of this process arises as a n → ∞ weak limit of the process started at time -1/2 log n with n clusters of mass 1/n… 

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