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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, 127-148 p.Article in journal (Refereed) Published
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Text
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, 127-148 p.
Keyword [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: diva2:919223
Available from: 2016-04-13 Created: 2016-04-07 Last updated: 2017-11-30Bibliographically approved

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Analysis and Probability Theory
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