The distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous planar anisotropic STIT Tessellations

Christoph Thäle

Commentationes Mathematicae Universitatis Carolinae (2010)

  • Volume: 51, Issue: 3, page 503-512
  • ISSN: 0010-2628

Abstract

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A result about the distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous and isotropic random tessellations stable under iteration (STIT tessellations) is extended to the anisotropic case using recent findings from Schreiber/Thäle, Typical geometry, second-order properties and central limit theory for iteration stable tessellations, arXiv:1001.0990 [math.PR] (2010). Moreover a new expression for the values of this probability distribution is presented in terms of the Gauss hypergeometric function 2 F 1 .

How to cite

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Thäle, Christoph. "The distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous planar anisotropic STIT Tessellations." Commentationes Mathematicae Universitatis Carolinae 51.3 (2010): 503-512. <http://eudml.org/doc/38146>.

@article{Thäle2010,
abstract = {A result about the distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous and isotropic random tessellations stable under iteration (STIT tessellations) is extended to the anisotropic case using recent findings from Schreiber/Thäle, Typical geometry, second-order properties and central limit theory for iteration stable tessellations, arXiv:1001.0990 [math.PR] (2010). Moreover a new expression for the values of this probability distribution is presented in terms of the Gauss hypergeometric function $\{_2F_1\}$.},
author = {Thäle, Christoph},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {hypergeometric function; iteration/nesting; random tessellation; segments; stochastic geometry; stochastic stability; random tessellation; hypergeometric function},
language = {eng},
number = {3},
pages = {503-512},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous planar anisotropic STIT Tessellations},
url = {http://eudml.org/doc/38146},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Thäle, Christoph
TI - The distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous planar anisotropic STIT Tessellations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 3
SP - 503
EP - 512
AB - A result about the distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous and isotropic random tessellations stable under iteration (STIT tessellations) is extended to the anisotropic case using recent findings from Schreiber/Thäle, Typical geometry, second-order properties and central limit theory for iteration stable tessellations, arXiv:1001.0990 [math.PR] (2010). Moreover a new expression for the values of this probability distribution is presented in terms of the Gauss hypergeometric function ${_2F_1}$.
LA - eng
KW - hypergeometric function; iteration/nesting; random tessellation; segments; stochastic geometry; stochastic stability; random tessellation; hypergeometric function
UR - http://eudml.org/doc/38146
ER -

References

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  1. Abramowitz M., Stegun I.A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1965, online version under http://www.math.ucla.edu/ cbm/aands/index.htm. Zbl0643.33001MR1225604
  2. Mecke J., Nagel W., Weiss V., 10.3103/S1068362307010025, J. Contemp. Math. Anal. 42 (2007), 28–43. Zbl1155.60005MR2361580DOI10.3103/S1068362307010025
  3. Mecke J., Nagel W., Weiss V., Some distributions for I-segments of planar random homogeneous STIT tessellations, Math. Nachr. (2010)(to appear). MR2832660
  4. Nagel W., Weiss V., 10.1239/aap/1134587744, Adv. in Appl. Probab. 37 (2005), 859–883. Zbl1098.60012MR2193987DOI10.1239/aap/1134587744
  5. Schneider R., Weil W., Stochastic and Integral Geometry, Springer, Berlin, 2008. Zbl1175.60003MR2455326
  6. Schreiber T., Thäle C., Typical geometry, second-order properties and central limit theory for iteration stable tessellations, arXiv:1001.0990 [math.PR] (2010). MR2796670
  7. Thäle C., 10.5566/ias.v28.p69-76, Image Anal. Stereol. 28 (2009), 69–76. MR2538063DOI10.5566/ias.v28.p69-76

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