Show simple item record

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorCorujo, Josué
HAL ID: 734995
ORCID: 0000-0002-3997-7391
dc.date.accessioned2021-11-23T13:01:59Z
dc.date.available2021-11-23T13:01:59Z
dc.date.issued2021
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22220
dc.language.isoenen
dc.subjectneutral multi-allelic Moran processen
dc.subjectFleming-Viot type particle systemen
dc.subjectinteracting particle systemen
dc.subjectconvergence rate to stationarityen
dc.subjectfinite continuous-time Markov chainsen
dc.subjectmultivariate Hahn polynomialsen
dc.subjectcutoffen
dc.subjectmultivariate Krawtchouk polynomialsen
dc.subject.ddc519en
dc.titleOn the spectrum and the ergodicity of a neutral multi-allelic Moran modelen
dc.title.alternativeSur le spectre et l'ergodicité d'un modèle Moran neutre multi-alléliqueen
dc.title.alternativeSobre el espectrum y la ergodicidad de un modelo neutro de Moranen
dc.typeDocument de travail / Working paper
dc.description.abstractenThe purpose of this paper is to provide a complete description of the eigenvalues of the generator of a neutral multi-type Moran model, and the applications to the study of the speed of convergence to stationarity. The Moran model we consider is a non-reversible in general, continuous-time Markov chain with unknown stationary distribution. Specifically, we consider N individuals such that each one of them is of one type among K possible allelic types. The individuals interact in two ways: by an independent irreducible mutation process and by a reproduction process, where a pair of individuals is randomly chosen, one of them dies and the other reproduces. Our main result provides explicit expressions for the eigenvalues of the infinitesimal generator matrix of the Moran process, in terms of the eigenvalues of the jump rate matrix. As consequences of this result, we study the convergence in total variation of the process to stationarity. Our results include a lower bound for the mixing time of the Moran process when the mutation process allows a real eigenvalue. Furthermore, we study in detail the spectral decomposition of the neutral multi-allelic Moran model with parent independent mutation scheme, which turns to be the unique mutation scheme that makes the neutral Moran process reversible. Under the parent independent mutation, we also prove the existence of a cutoff phenomenon in the chi-square and the total variation distances when initially all the individuals are of the same type and the number of individuals tends to infinity. Additionally, in the absence of reproduction, we prove that the the total variation distance to stationarity of the parent independent mutation process, when initially all the individuals are of the same type, has a Gaussian profile.en
dc.identifier.citationpages35en
dc.relation.ispartofseriestitleCahier de recherche du CEREMADEen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02969874en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.identifier.citationdate2021
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2021-11-23T12:57:44Z
hal.author.functionaut


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record