Arak-Clifford-Surgailis Tessellations. Basic Properties and Variance of the Total Edge Length

Autor(en): Thaele, Christoph
Stichwörter: Gibbs modification; MARKOV-FIELDS; Pair-correlation function; Physics; Physics, Mathematical; Polygonal Markov field; Random tessellation; Stochastic geometry
Erscheinungsdatum: 2011
Herausgeber: SPRINGER
Journal: JOURNAL OF STATISTICAL PHYSICS
Volumen: 144
Ausgabe: 6
Startseite: 1329
Seitenende: 1339
Zusammenfassung: 
Non-homogeneous random tessellations in the plane with T-shaped vertices are considered, which are defined as Gibbsian modifications of a Poisson line process with arbitrary locally finite intensity measure. In the homogeneous set-up they can be regarded as a specific case of the general Arak-Surgailis polygonal fields in the plane and share some properties with the iteration stable (STIT) tessellations. In the non-homogeneous and anisotropic environment an explicit expression for the partition function is provided and first-and second-order properties of the random length measure of the tessellations restricted to a convex sampling window are derived. In the more special isotropic regime a closed formula for the pair-correlation function and the variance of the total edge length is obtained.
ISSN: 00224715
DOI: 10.1007/s10955-011-0331-7

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