# 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…

## 153 Citations

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

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

The Entrance Boundary of the Multiplicative Coalescent

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