Distances Between Poisson k-Flats

DC FieldValueLanguage
dc.contributor.authorSchulte, Matthias
dc.contributor.authorThaele, Christoph
dc.date.accessioned2021-12-23T16:10:49Z-
dc.date.available2021-12-23T16:10:49Z-
dc.date.issued2014
dc.identifier.issn13875841
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/9408-
dc.description.abstractThe distances between flats of a Poisson k-flat process in the d-dimensional Euclidean space with k < d/2 are discussed. Continuing an approach originally due to Rolf Schneider, the number of pairs of flats having distance less than a given threshold and midpoint in a fixed compact and convex set is considered. For a family of increasing convex subsets, the asymptotic variance is computed and a central limit theorem with an explicit rate of convergence is proven. Moreover, the asymptotic distribution of the m-th smallest distance between two flats is investigated and it is shown that the ordered distances form asymptotically after suitable rescaling an inhomogeneous Poisson point process on the positive real half-axis. A similar result with a homogeneous limiting process is derived for distances around a fixed, strictly positive value. Our proofs rely on recent findings based on the Wiener-It chaos decomposition and the Malliavin-Stein method.
dc.description.sponsorshipGerman Academic Exchange Service (DAAD)Deutscher Akademischer Austausch Dienst (DAAD); This paper was written while the first author was visiting Case Western Reserve University. He was supported by the German Academic Exchange Service (DAAD).
dc.language.isoen
dc.publisherSPRINGER
dc.relation.ispartofMETHODOLOGY AND COMPUTING IN APPLIED PROBABILITY
dc.subjectCentral limit theorem
dc.subjectChaos decomposition
dc.subjectExtreme values
dc.subjectLIMIT
dc.subjectLimit theorems
dc.subjectMathematics
dc.subjectPoisson flat process
dc.subjectPoisson point process
dc.subjectPoisson U-statistic
dc.subjectStatistics & Probability
dc.subjectStochastic geometry
dc.subjectWiener-Ito integral
dc.titleDistances Between Poisson k-Flats
dc.typejournal article
dc.identifier.doi10.1007/s11009-012-9319-2
dc.identifier.isiISI:000335508800005
dc.description.volume16
dc.description.issue2, SI
dc.description.startpage311
dc.description.endpage329
dc.identifier.eissn15737713
dc.publisher.placeVAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS
dcterms.isPartOf.abbreviationMethodol. Comput. Appl. Probab.
dcterms.oaStatusGreen Submitted
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