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The standard additive coalescent

1998
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Annals of Probability
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Regard an element of the set = 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 -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. We show this standard

doi:10.1214/aop/1022855879
fatcat:bpcex5ubtbckjewgy2eagyauay