Joint distribution of direction and length of typical I-segment in a homogeneous random planar tessellation stable under iteration

Journal of Contemporary Mathematical Analysis

Volumn 44, Issue 1, 2009, Pages 45-53

  Mecke, J ^a  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

Iteration nesting of tessellations; Random tessellation; Stability of distributions; Stochastic geometry

Indexed keywords

EID: 77952899078     PISSN: 10683623     EISSN: 19349416     Source Type: Journal    
DOI: 10.3103/S1068362309010087     Document Type: Article

References (11)

1. R. V. Ambartzumian, "A note on pseudometrics on the plane," Z. Wahrscheinlichkeitstheorie verw. Geb. 37, 145-155 1976.
2. R. V. Ambartzumian, Combinatorial Integral Geometry with Applications to Mathematical Stereology (John Wiley and Sons, Chichester, 1982).
3. R. E. Miles and M. S. Mackisack, "A large class of random tessellations with the classic Poisson polygon distributions," Forma 17, 1-17 (2002).
4. W. Nagel and V. Weiss, "Limits of sequences of stationary planar tessellations," Adv. Appl. Prob. (SGSA) 35, 123-138 (2003).
5. W. Nagel and V. Weiss, "Crack STIT tessellations - Existence and uniqueness of tessellations that are stable with respect to iterations," Izvestija Akademii Nauk Armenii, Matematika 39(4), 84-114 (2004).
6. W. Nagel and V. Weiss, "Crack STIT tessellations: Characterization of the stationary random tessellations stable with respect to iteration," Adv. Appl. Prob. (SGSA) 37, 859-883 (2005).
7. W. Nagel and V. Weiss, "STIT tessellations in the plane," Rendiconti del circulo matematico di Palermo, Serie II 77, 441-458 (2006).
8. J. Mecke, W. Nagel and V. Weiss, "Length distributions of edges in planar stationary and isotropic STIT tessellations," Izvestija Akademii Nauk Armenii, Matematika 42(1), 39-60 (2007).
9. J. Mecke, W. Nagel and V. Weiss, "A global construction of homogeneous random planar tessellations that are stable under iteration," Stochastics: An International Journal of Probability and Stochastic Processes 80(1), 51-67 (2008).
10. J. Mecke, W. Nagel and V. Weiss, "The iteration of randomtessellations and a construction of a homogeneous process of cell divisions," Adv. Appl. Prob. (SGSA) 40, 49-59 (2008).
11. R. Schneider and W. Weil, Stochastic and Integral Geometry (Springer, Berlin, 2008).