DC FieldValueLanguage
dc.contributor.authorLast, Günter-
dc.contributor.authorNestmann, Franz-
dc.contributor.authorSchulte, Matthias-
dc.date.accessioned2022-03-04T13:41:32Z-
dc.date.available2022-03-04T13:41:32Z-
dc.date.issued2021-02-
dc.identifier.citationAnnals of Applied Probability 31 (1): 128-168 (2021-02)de_DE
dc.identifier.issn1050-5164de_DE
dc.identifier.urihttp://hdl.handle.net/11420/11811-
dc.description.abstractThe random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study first and second order properties of the numbers of components isomorphic to given finite connected graphs. For increasing observation windows in an Euclidean setting we prove qualitative multivariate and quantitative univariate central limit theorems for these component counts as well as a qualitative central limit theorem for the total number of finite components. To this end we first derive general results for functions of edge marked Poisson processes, which we believe to be of independent interest.en
dc.language.isoende_DE
dc.relation.ispartofThe annals of applied probabilityde_DE
dc.subjectCentral limit theoremde_DE
dc.subjectComponent countde_DE
dc.subjectCovariance structurede_DE
dc.subjectEdge markingde_DE
dc.subjectGilbert graphde_DE
dc.subjectPoisson processde_DE
dc.subjectRandom connection modelde_DE
dc.subjectRandom geometric graphde_DE
dc.titleThe random connection model and functions of edge-marked poisson processes: Second order properties and normal approximationde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.englishThe random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study first and second order properties of the numbers of components isomorphic to given finite connected graphs. For increasing observation windows in an Euclidean setting we prove qualitative multivariate and quantitative univariate central limit theorems for these component counts as well as a qualitative central limit theorem for the total number of finite components. To this end we first derive general results for functions of edge marked Poisson processes, which we believe to be of independent interest.de_DE
tuhh.publisher.doi10.1214/20-AAP1585-
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.issue1de_DE
tuhh.container.volume31de_DE
tuhh.container.startpage128de_DE
tuhh.container.endpage168de_DE
dc.identifier.scopus2-s2.0-85103273104-
datacite.resourceTypeJournal Article-
datacite.resourceTypeGeneralText-
item.grantfulltextnone-
item.cerifentitytypePublications-
item.openairetypeArticle-
item.creatorOrcidLast, Günter-
item.creatorOrcidNestmann, Franz-
item.creatorOrcidSchulte, Matthias-
item.languageiso639-1en-
item.creatorGNDLast, Günter-
item.creatorGNDNestmann, Franz-
item.creatorGNDSchulte, Matthias-
item.fulltextNo Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.mappedtypeArticle-
crisitem.author.deptMathematik E-10-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik (E)-
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