@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#> .

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    dct:description """
              We consider a periodic planar Lorentz process with strictly convex obstacles and finite horizon. This process describes the displacement of a particle moving in the plane with unit speed and with elastic reflection on the obstacles. We call number of self-intersections of this Lorentz process the number V(n) of couples of integers (k,m) smaller than n such that the particle hits a same obstacle both at the k-th and at the m-th collision times. The aim of this paper is to prove that the variance of V(n) is equivalent to cn^2 (such a result has recently been proved for simple planar random walks by Deligiannidis and Utev).
            """ ;
    dct:identifier "hal-00799504" ;
    dct:issued "2026-05-12T23:58:28.926792"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-12T23:58:28.926798"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "An asymptotic estimate of the variance of the self-intersections of a planar periodic Lorentz process" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00799504v1/resource/7946163b-a474-43a6-a62e-d8766170a402> ;
    dcat:keyword "infoeu-reposemanticspreprint",
        "lorentz-process",
        "mathmath-dsmathematics-mathdynamical-systems-mathds",
        "mathmath-prmathematics-mathprobability-mathpr",
        "msc-60f99--37d50",
        "preprints-working-papers-",
        "self-intersection",
        "sinai-billiard",
        "variance" ;
    dcat:landingPage <https://hal.science/hal-00799504> .

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    dct:format "HTML" ;
    dct:issued "2026-05-12T23:58:28.946569"^^xsd:dateTime ;
    dct:modified "2026-05-12T23:58:28.902836"^^xsd:dateTime ;
    dct:title "An asymptotic estimate of the variance of the self-intersections of a planar periodic Lorentz process" ;
    dcat:accessURL <https://hal.science/hal-00799504> .

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    foaf:name "test_moissonnage_selune" .

<https://hal.science/hal-00799504> a foaf:Document .