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On the Intersection Density of Flat Processes
Author(s) -
Mecke J.
Publication year - 1991
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19911510106
Subject(s) - intersection (aeronautics) , mathematics , poisson distribution , poisson process , euclidean space , euclidean geometry , intensity (physics) , process (computing) , space (punctuation) , geometry , poisson point process , combinatorics , mathematical analysis , statistics , physics , computer science , optics , transport engineering , operating system , engineering
Stationary POISSON r ‐flat processes in the d ‐dimensional Euclidean space ( d /2 ≦ r ≦ d − 1) induce a process of (2 r − d )‐flats each of which is the intersection of two r ‐flats of the original processes. The intensity of the induced (2 r − d )‐flat process is called intersection density of the original POISSON r ‐flat process. The problem of maximizing the intersection density for given intensity is considered. A new approach to earlier results of THOMAS and the author is presented.