On Asymptotics of Exchangeable Coalescents with Multiple Collisions

@inproceedings{Gnedin2008OnAO,
  title={On Asymptotics of Exchangeable Coalescents with Multiple Collisions},
  author={Alexander Gnedin},
  year={2008}
}
We study the number of collisions, Xn, of an exchangeable coalescent with multiple collisions ( -coalescent) which starts withn particles and is driven by rates determined by a finite characteristic measure ν(dx) = x−2 (dx). Via a coupling technique, we derive limiting laws of Xn, using previous results on regenerative compositions derived from stick-breaking partitions of the unit interval. The possible limiting laws of Xn include normal, stable with index 1 ≤ α < 2, and Mittag–Leffler… CONTINUE READING

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