@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-00814105v2> a dcat:Dataset ;
    dct:description """
              Let $\\Cal S$ be an abelian finitely generated semigroup of endomorphisms of a probability space $(\\Omega, {\\Cal A}, \\mu)$, with $(T_1, ..., T_d)$ a system of generators in ${\\Cal S}$. Given an increasing sequence of domains $(D_n) \\subset \\N^d$, a question is the convergence in distribution of the normalized sequence $|D_n|^{-\\frac12} \\sum_{{\\k} \\, \\in D_n} \\, f \\circ T^{\\,{\\k}}$, for $f \\in L^2_0(\\mu)$, where $T^{\\k}= T_1^{k_1} ... T_d^{k_d}$, ${\\k}= (k_1, ..., k_d) \\in {\\N}^d$. After a preliminary spectral study when the action of $\\Cal S$ has a Lebesgue spectrum, we consider $\\N^d$- or $\\Z^d$-actions given by commuting toral automorphisms or endomorphisms on $\\T^\\rho$, $\\rho \\geq 1$. For a totally ergodic action by automorphisms, we show a CLT for the above normalized sequence or other summation methods like barycenters, as well as a criterion of non-degeneracy of the variance, when $f$ is regular on the torus. A CLT is also proved for some semigroups of endomorphisms. Classical results on the existence and the construction of such actions by automorphisms are recalled.
            """ ;
    dct:identifier "hal-00814105" ;
    dct:issued "2026-05-11T02:55:22.470999"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-11T02:55:22.471003"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Central limit theorem for commutative semigroups of toral endomorphisms" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00814105v2/resource/c285dc66-712f-40b0-8685-2956af10a6d2> ;
    dcat:keyword "60f05-28d05-22d40-47a35-47b15",
        "central-limit-theorem",
        "group-of-toral-automorphisms",
        "infoeu-reposemanticspreprint",
        "k-system",
        "mathmath-dsmathematics-mathdynamical-systems-mathds",
        "moments-and-mixing",
        "preprints-working-papers-",
        "rotated-process",
        "s-units",
        "semigroup-of-endomorphisms",
        "zd-action" ;
    dcat:landingPage <https://hal.science/hal-00814105> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00814105v2/resource/c285dc66-712f-40b0-8685-2956af10a6d2> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-11T02:55:22.473260"^^xsd:dateTime ;
    dct:modified "2026-05-11T02:55:22.451518"^^xsd:dateTime ;
    dct:title "Central limit theorem for commutative semigroups of toral endomorphisms" ;
    dcat:accessURL <https://hal.science/hal-00814105> .

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

<https://hal.science/hal-00814105> a foaf:Document .