On the number of collisions in beta(2, b)-coalescents
Alex Iksanov, Alex Marynych, and Martin Möhle
Source: Bernoulli Volume 15, Number 3
(2009), 829-845.
Abstract
Expansions are provided for the moments of the number of collisions Xn in the β(2, b)-coalescent restricted to the set {1, …, n}. We verify that converges almost surely to one and that Xn, properly normalized, weakly converges to the standard normal law. These results complement previously known facts concerning the number of collisions in β(a, b)-coalescents with a∈(0, 2) and b=1, and a>2 and b>0. The case a=2 is a kind of ‘border situation’ which seems not to be amenable to approaches used for a≠2.
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Keywords: asymptotics of moments; beta-coalescent; number of collisions; random regenerative composition; recursion with random indices
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Permanent link to this document: http://projecteuclid.org/euclid.bj/1251463283
Digital Object Identifier: doi:10.3150/09-BEJ192
Zentralblatt MATH identifier: 05815957
Mathematical Reviews number (MathSciNet): MR2555201
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