@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-00085782v1> a dcat:Dataset ;
    dct:description """
              We analyze the asymptotic behavior of random variables $x(n,x_0)$ defined by $x(0,x_0)=x_0$ and $x(n+1,x_0)=A(n)x(n,x_0)$, where $\\sAn$ is a stationary and ergodic sequence of random matrices with entries in the semi-ring \\mbox{$\\R\\cup\\{-\\infty\\}$} whose addition is the $\\max$ and whose multiplication is $+$. Such sequences modelize a large class of discrete event systems, among which timed event graphs, 1-bounded Petri nets, some queuing networks, train or computer networks. We give necessary conditions for $\\left(\\frac{1}{n}x(n,x_0)\\right)_{n\\in\\N}$ to converge almost surely. Then, we prove a general scheme to give partial converse theorems. When $\\max_{A_{ij}(0)\\neq -\\infty}|A_{ij}(0)|$ is integrable, it allows us: - to give a necessary and sufficient condition for the convergence of $\\left(\\frac{1}{n}x(n,0)\\right)_{n\\in\\N}$ when the sequence $\\left(A(n) \\right)_{n\\in\\N}$ is i.i.d., - to prove that, if $\\left(A(n) \\right)_{n\\in\\N}$ satisfy a condition of reinforced ergodicity and a condition of fixed structure (i.e. $\\P\\left(A_{ij}(0)=-\\infty\\right)\\in\\{0,1\\}$), then $\\left(\\frac{1}{n}x(n,0)\\right)_{n\\in\\N}$ converges almost-surely, - and to reprove the convergence of $\\left(\\frac{1}{n}x(n,0)\\right)_{n\\in\\N}$ if the diagonal entries are never $-\\infty$.
            """ ;
    dct:identifier "hal-00085782" ;
    dct:issued "2026-05-09T21:31:41.568727"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-09T21:31:41.568733"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Law of Large Numbers for products of random matrices with coefficients in the max-plus semi-ring." ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00085782v1/resource/f63d48fa-c524-417e-a629-17d0622f086a> ;
    dcat:keyword "discrete-event-systems",
        "infoeu-reposemanticspreprint",
        "law-of-large-numbers",
        "mathmath-prmathematics-mathprobability-mathpr",
        "max-plus",
        "msc--60f15-90b15-93c65-93e15",
        "preprints-working-papers-",
        "products-of-random-matrices",
        "stochastic-recurrent-sequences" ;
    dcat:landingPage <https://hal.science/hal-00085782> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00085782v1/resource/f63d48fa-c524-417e-a629-17d0622f086a> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-09T21:31:41.577647"^^xsd:dateTime ;
    dct:modified "2026-05-09T21:31:41.559761"^^xsd:dateTime ;
    dct:title "Law of Large Numbers for products of random matrices with coefficients in the max-plus semi-ring." ;
    dcat:accessURL <https://hal.science/hal-00085782> .

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    foaf:name "test_moissonnage_selune" .

<https://hal.science/hal-00085782> a foaf:Document .