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Asymptotics of the Minimal Clade Size and Related Functionals of Certain Beta-Coalescents
Univ Guanajuato, Dept Matemat, Calle Jalisco S-N Col, Guanajuato 36240, Mexico..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, Vol. 142, no 1, p. 127-148Article in journal (Refereed) Published
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Abstract [en]

The Beta(2-alpha,alpha) n-coalescent with 1 <alpha < 2 is a Markov process taking values in the set of partitions of {1,aEuro broken vertical bar,n}. It evolves from the initial value {1},aEuro broken vertical bar,{n} by merging (coalescing) blocks together into one and finally reaching the absorbing state {1,aEuro broken vertical bar,n}. This article aims to give the asymptotic distribution of the size of the minimal clade of 1, which is the block containing 1 at the time of coalescence of the singleton {1}. To this, we express it as a function of the coalescence time of {1}, the number of blocks involved and their sizes. The asymptotic behaviours of those related functionals are therefore also studied.

Place, publisher, year, edition, pages
2016. Vol. 142, no 1, p. 127-148
Keywords [en]
Beta-coalescent, Ranked Lambda-coalescent, Kingman's paintbox construction, Minimal clade size, External branch lengths, Block-counting process
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-282785DOI: 10.1007/s10440-015-0020-7ISI: 000371629600009OAI: oai:DiVA.org:uu-282785DiVA, id: diva2:919223
Available from: 2016-04-13 Created: 2016-04-07 Last updated: 2017-11-30Bibliographically approved

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