The standard additive coalescent

Abstract

Regard an element of the set Δ := {(x1, x2, . . .): x1 ≥ x2 ≥ ⋯ ≥ 0, ∑i xi = 1} as a fragmentation of unit mass into clusters of masses xi. The additive coalescent of Evans and Pitman is the Δ-valued Markov process in which pairs of clusters of masses {xi, x j} merge into a cluster of mass xi + x j at rate xi + x j. They showed that a version (X∞(t), -∞ < t