Author:
McSweeney John K.,Pittel Boris G.
Abstract
We study a process where balls are repeatedly thrown intonboxes independently according to some probability distributionp. We start withnballs, and at each step, all balls landing in the same box are fused into a single ball; the process terminates when there is only one ball left (coalescence). Letc:= ∑jpj2, the collision probability of two fixed balls. We show that the expected coalescence time is asymptotically 2c−1, under two constraints onpthat exclude a thin set of distributionsp. One of the constraints isc=o(ln−2n). This ln−2nis shown to be a threshold value: forc= ω(ln−2n), there existspwithc(p) =csuch that the expected coalescence time far exceedsc−1. Connections to coalescent processes in population biology and theoretical computer science are discussed.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
1 articles.
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