Asymptotics of the frequency spectrum for general Dirichlet Ξ-coalescents

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• dc.contributor.author González-Casanova, Adrián
• dc.contributor.author Miró Pina, Verónica
• dc.contributor.author Schertzer, Emmanuel
• dc.contributor.author Siri-Jégousse, Arno
• dc.date.accessioned 2024-03-19T07:29:04Z
• dc.date.available 2024-03-19T07:29:04Z
• dc.date.issued 2024
• dc.description.abstract In this work, we study general Dirichlet coalescents, which are a family of Ξ-coalecents constructed from i.i.d mass partitions, and are an extension of the symmetric coalescent. This class of models is motivated by population models with recurrent demographic bottlenecks. We study the short time behavior of the multidimensional block counting process whose ith component counts the number of blocks of size i. Compared to standard coalescent models (such as the class of Λ-coalescents coming down from infinity), our process has no deterministic speed of coming down from infinity. In particular, we prove that, under appropriate re-scaling, it converges to a stochastic process which is the unique solution of a martingale problem. We show that the multivariate Lamperti transform of this limiting process is a Markov Additive Process (MAP). This allows us to provide some asymptotics for the n-Site Frequency Spectrum, which is a statistic widely used in population genetics. In particular, the rescaled number of mutations converges to the exponential functional of a subordinator.
• dc.format.mimetype application/pdf
• dc.identifier.citation González A, Miró V, Schertzer E, Siri-Jégousse A. Asymptotics of the frequency spectrum for general Dirichlet Ξ-coalescents. Electron J Probab. 2024 Jan 1;29:1-35. DOI: 10.1214/23-ejp1064
• dc.identifier.doi http://dx.doi.org/10.1214/23-ejp1064
• dc.identifier.issn 1083-6489
• dc.identifier.uri http://hdl.handle.net/10230/59472
• dc.language.iso eng
• dc.publisher Institute of Mathematical Statistics
• dc.relation.ispartof Electronic Journal of Probability. 2024 Jan 1;29:1-35
• dc.rights Creative Commons Attribution 4.0 International License.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Coalescent processes
• dc.subject.keyword Coming down form infinity
• dc.subject.keyword Markov additive processes
• dc.subject.keyword Partitions
• dc.subject.keyword Subordinator
• dc.title Asymptotics of the frequency spectrum for general Dirichlet Ξ-coalescents
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion