@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-00768343v1> a dcat:Dataset ;
    dct:description """
              We study the asymptotic behavior af the number of cuts $X(T_n)$ needed to isolate the root in a rooted binary random tree $T_n$ with $n$ leaves. We focus on the case of subtrees of the Continuum Random Tree generated by uniform sampling of leaves. We elaborate on a recent result by Abraham and Delmas, who showed that $X(T_n)/\\sqrt{2n}$ converges a.s. towards a Rayleigh-distributed random variable $\\Theta$, which gives a continuous analog to an earlier result by Janson on conditioned, finite-variance Galton-Watson trees. We prove a convergence in distribution of $n^{-1/4}(X(T_n)-\\sqrt{2n}\\Theta)$ towards a random mixture of Gaussian variables. The proofs use martingale limit theory for random processes defined on the CRT, related to the theory of records of Poisson point processes.
            """ ;
    dct:identifier "hal-00768343" ;
    dct:issued "2026-05-29T16:47:21.402328"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-29T16:47:21.402335"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Fluctuations for the number of records on subtrees of the Continuum Random Tree" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00768343v1/resource/cdaa65e8-b086-46cf-8e5e-67609fad43aa> ;
    dcat:keyword "60f05--60g55--60j80",
        "central-limit-theorem",
        "continuum-random-tree",
        "infoeu-reposemanticspreprint",
        "mathmath-prmathematics-mathprobability-mathpr",
        "point-processes",
        "preprints-working-papers-",
        "records" ;
    dcat:landingPage <https://hal.science/hal-00768343> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00768343v1/resource/cdaa65e8-b086-46cf-8e5e-67609fad43aa> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-29T16:47:21.456050"^^xsd:dateTime ;
    dct:modified "2026-05-29T16:47:21.374061"^^xsd:dateTime ;
    dct:title "Fluctuations for the number of records on subtrees of the Continuum Random Tree" ;
    dcat:accessURL <https://hal.science/hal-00768343> .

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

<https://hal.science/hal-00768343> a foaf:Document .