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Some distributions for I‐segments of planar random homogeneous STIT tessellations
Author(s) -
Mecke J.,
Nagel W.,
Weiß V.
Publication year - 2011
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.200810221
Subject(s) - tessellation (computer graphics) , mathematics , planar , homogeneous , isotropy , geometry , combinatorics , division (mathematics) , distribution (mathematics) , mathematical analysis , computer science , physics , optics , computer graphics (images) , arithmetic
A tessellation‐valued process is considered, the random states of which are planar random homogeneous tessellations stable under iteration (STIT). It can be interpreted as a process of subsequent division of cells by random chords. These chords, referred to as I‐segments, have a length and a birth time. In the present paper the joint distribution of the length and the birth time of the typical I‐segment for isotropic STIT tessellations is given. Furthermore, later occurring chords have their endpoints in the relative interior of an I‐segment and thus generate a node of the tessellation. The distribution of the number of nodes in the relative interior of the typical I‐segment is studied. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim