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.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