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August 2009 On the number of collisions in beta $(2, b)$-coalescents
Alex Iksanov, Alex Marynych, Martin Möhle
Bernoulli 15(3): 829-845 (August 2009). DOI: 10.3150/09-BEJ192

Abstract

Expansions are provided for the moments of the number of collisions $X_n$ in the $β(2, b)$-coalescent restricted to the set $\{1, …, n\}$. We verify that $X_{n}/\mathbb{E}X_{n}$ converges almost surely to one and that $X_n$, 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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Alex Iksanov. Alex Marynych. Martin Möhle. "On the number of collisions in beta $(2, b)$-coalescents." Bernoulli 15 (3) 829 - 845, August 2009. https://doi.org/10.3150/09-BEJ192

Information

Published: August 2009
First available in Project Euclid: 28 August 2009

zbMATH: 1208.60081
MathSciNet: MR2555201
Digital Object Identifier: 10.3150/09-BEJ192

Keywords: asymptotics of moments , beta-coalescent , number of collisions , random regenerative composition , recursion with random indices

Rights: Copyright © 2009 Bernoulli Society for Mathematical Statistics and Probability

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Vol.15 • No. 3 • August 2009
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