FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4385989107> ?p ?o ?g. }

• W4385989107 endingPage "129" @default.
• W4385989107 startingPage "96" @default.
• W4385989107 abstract "Poisson processes in the space of k-dimensional totally geodesic subspaces (k-flats) in a d-dimensional standard space of constant curvature κ∈{−1,0,1} are studied, whose distributions are invariant under the isometries of the space. We consider the intersection processes of order m together with their (d−m(d−k))-dimensional Hausdorff measure within a geodesic ball of radius r. Asymptotic normality for fixed r is shown as the intensity of the underlying Poisson process tends to infinity for all m satisfying d−m(d−k)≥0. For κ∈{−1,0} the problem is also approached in the set-up where the intensity is fixed and r tends to infinity. Again, if 2k≤d+1 a central limit theorem is shown for all possible values of m. However, while for κ=0 asymptotic normality still holds if 2k>d+1, we prove for κ=−1 convergence to a non-Gaussian infinitely divisible limit distribution in the special case m=1. The proof of asymptotic normality is based on the analysis of variances and general bounds available from the Malliavin–Stein method. We also show for general κ∈{−1,0,1} that, roughly speaking, the variances within a general observation window W are maximal if and only if W is a geodesic ball having the same volume as W. Along the way we derive a new integral-geometric formula of Blaschke–Petkantschin type in a standard space of constant curvature." @default.
• W4385989107 created "2023-08-19" @default.
• W4385989107 creator A5012833395 @default.
• W4385989107 creator A5013850827 @default.
• W4385989107 creator A5045045693 @default.
• W4385989107 date "2023-11-01" @default.
• W4385989107 modified "2023-10-14" @default.
• W4385989107 title "Intersections of Poisson <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline id=d1e184 altimg=si24.svg><mml:mi>k</mml:mi></mml:math>-flats in constant curvature spaces" @default.
• W4385989107 cites W1659004305 @default.
• W4385989107 cites W1976544009 @default.
• W4385989107 cites W1985612411 @default.
• W4385989107 cites W1987278905 @default.
• W4385989107 cites W2020340581 @default.
• W4385989107 cites W2023971197 @default.
• W4385989107 cites W2024866211 @default.
• W4385989107 cites W2028534697 @default.
• W4385989107 cites W2085996269 @default.
• W4385989107 cites W2113377426 @default.
• W4385989107 cites W2127132699 @default.
• W4385989107 cites W2162337698 @default.
• W4385989107 cites W2166690459 @default.
• W4385989107 cites W2275286668 @default.
• W4385989107 cites W2289468624 @default.
• W4385989107 cites W2808453398 @default.
• W4385989107 cites W2963049699 @default.
• W4385989107 cites W2963420700 @default.
• W4385989107 cites W2964261504 @default.
• W4385989107 cites W3044005723 @default.
• W4385989107 cites W3110690976 @default.
• W4385989107 cites W3119690481 @default.
• W4385989107 cites W3121391808 @default.
• W4385989107 cites W3137476712 @default.
• W4385989107 cites W3163902834 @default.
• W4385989107 cites W3180883690 @default.
• W4385989107 cites W3184735480 @default.
• W4385989107 cites W3195958782 @default.
• W4385989107 cites W3198606567 @default.
• W4385989107 cites W4213171111 @default.
• W4385989107 cites W4231565812 @default.
• W4385989107 doi "https://doi.org/10.1016/j.spa.2023.08.001" @default.
• W4385989107 hasPublicationYear "2023" @default.
• W4385989107 type Work @default.
• W4385989107 citedByCount "0" @default.
• W4385989107 crossrefType "journal-article" @default.
• W4385989107 hasAuthorship W4385989107A5012833395 @default.
• W4385989107 hasAuthorship W4385989107A5013850827 @default.
• W4385989107 hasAuthorship W4385989107A5045045693 @default.
• W4385989107 hasBestOaLocation W43859891072 @default.
• W4385989107 hasConcept C114614502 @default.
• W4385989107 hasConcept C134306372 @default.
• W4385989107 hasConcept C165818556 @default.
• W4385989107 hasConcept C195065555 @default.
• W4385989107 hasConcept C2524010 @default.
• W4385989107 hasConcept C2779668893 @default.
• W4385989107 hasConcept C33923547 @default.
• W4385989107 hasConceptScore W4385989107C114614502 @default.
• W4385989107 hasConceptScore W4385989107C134306372 @default.
• W4385989107 hasConceptScore W4385989107C165818556 @default.
• W4385989107 hasConceptScore W4385989107C195065555 @default.
• W4385989107 hasConceptScore W4385989107C2524010 @default.
• W4385989107 hasConceptScore W4385989107C2779668893 @default.
• W4385989107 hasConceptScore W4385989107C33923547 @default.
• W4385989107 hasFunder F4320320879 @default.
• W4385989107 hasLocation W43859891071 @default.
• W4385989107 hasLocation W43859891072 @default.
• W4385989107 hasOpenAccess W4385989107 @default.
• W4385989107 hasPrimaryLocation W43859891071 @default.
• W4385989107 hasRelatedWork W1973901587 @default.
• W4385989107 hasRelatedWork W1995601874 @default.
• W4385989107 hasRelatedWork W2044124817 @default.
• W4385989107 hasRelatedWork W2150448166 @default.
• W4385989107 hasRelatedWork W2553783225 @default.
• W4385989107 hasRelatedWork W2595699648 @default.
• W4385989107 hasRelatedWork W2948699889 @default.
• W4385989107 hasRelatedWork W3111769232 @default.
• W4385989107 hasRelatedWork W4288337536 @default.
• W4385989107 hasRelatedWork W4313484206 @default.
• W4385989107 hasVolume "165" @default.
• W4385989107 isParatext "false" @default.
• W4385989107 isRetracted "false" @default.
• W4385989107 workType "article" @default.