caa a22 4500 445391030 CHVBK 20180317143046.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s10955-011-0331-7 doi (NATIONALLICENCE)springer-10.1007/s10955-011-0331-7 Thäle Christoph Institut für Mathematik der Universität Osnabrück, Albrechtstraße 28a, 49076, Osnabrück, Germany aut Arak-Clifford-Surgailis Tessellations. Basic Properties and Variance of the Total Edge Length [Elektronische Daten] [Christoph Thäle] 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. Springer Science+Business Media, LLC, 2011 Gibbs modification nationallicence Pair-correlation function nationallicence Polygonal Markov field nationallicence Random tessellation nationallicence Stochastic geometry nationallicence Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/6(2011-09-01), 1329-1339 0022-4715 144:6<1329 2011 144 10955 https://doi.org/10.1007/s10955-011-0331-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-011-0331-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Thäle Christoph Institut für Mathematik der Universität Osnabrück, Albrechtstraße 28a, 49076, Osnabrück, Germany aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/6(2011-09-01), 1329-1339 0022-4715 144:6<1329 2011 144 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer