@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00674190v3> a dcat:Dataset ;
    dct:description """
              We consider a ${\\Lambda}$-coalescent and we study the asymptotic behavior of the total length $L^{(n)}_{ext}$ of the external branches of the associated $n$-coalescent. For Kingman coalescent, i.e. ${\\Lambda}={\\delta}_0$, the result is well known and is useful, together with the total length $L^{(n)}$, for Fu and Li's test of neutrality of mutations% under the infinite sites model asumption . For a large family of measures ${\\Lambda}$, including Beta$(2-{\\alpha},{\\alpha})$ with $0<\\alpha<1$, M{ö}hle has proved asymptotics of $L^{(n)}_{ext}$. Here we consider the case when the measure ${\\Lambda}$ is Beta$(2-{\\alpha},{\\alpha})$, with $1<\\alpha<2$. We prove that $n^{{\\alpha}-2}L^{(n)}_{ext}$ converges in $L^2$ to $\\alpha(\\alpha-1)\\Gamma(\\alpha)$. As a consequence, we get that $L^{(n)}_{ext}/L^{(n)}$ converges in probability to $2-\\alpha$. To prove the asymptotics of $L^{(n)}_{ext}$, we use a recursive construction of the $n$-coalescent by adding individuals one by one. Asymptotics of the distribution of $d$ normalized external branch lengths and a related moment result are also given.
            """ ;
    dct:identifier "hal-00674190" ;
    dct:issued "2026-05-11T01:15:47.207919"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-11T01:15:47.207923"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Asympotic behavior of the total length of external branches for Beta-coalescents" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00674190v3/resource/6c589bf3-b49e-44d3-bf7f-171ee058f4d9> ;
    dcat:keyword "ams-2010-60j28-60j25-92d25-60j85",
        "beta-coalescent",
        "block-counting-process",
        "coalescent-process",
        "fu-and-lis-statistical-test",
        "infoeu-reposemanticspreprint",
        "mathmath-prmathematics-mathprobability-mathpr",
        "preprints-working-papers-",
        "recursive-construction",
        "sdvgengpolife-sciences-q-biogeneticspopulations-and-evolution-q-biope",
        "total-length-of-external-branches" ;
    dcat:landingPage <https://hal.science/hal-00674190> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00674190v3/resource/6c589bf3-b49e-44d3-bf7f-171ee058f4d9> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-11T01:15:47.228147"^^xsd:dateTime ;
    dct:modified "2026-05-11T01:15:47.196076"^^xsd:dateTime ;
    dct:title "Asympotic behavior of the total length of external branches for Beta-coalescents" ;
    dcat:accessURL <https://hal.science/hal-00674190> .

<https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> a foaf:Agent ;
    foaf:name "test_moissonnage_selune" .

<https://hal.science/hal-00674190> a foaf:Document .