| Title:
|
The distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous planar anisotropic STIT Tessellations (English) |
| Author:
|
Thäle, Christoph |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
503-512 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 ${_2F_1}$. (English) |
| Keyword:
|
hypergeometric function |
| Keyword:
|
iteration/nesting |
| Keyword:
|
random tessellation |
| Keyword:
|
segments |
| Keyword:
|
stochastic geometry |
| Keyword:
|
stochastic stability |
| MSC:
|
05B45 |
| MSC:
|
52A22 |
| MSC:
|
60D05 |
| MSC:
|
60G55 |
| idZBL:
|
Zbl 1224.60015 |
| idMR:
|
MR2741883 |
| . |
| Date available:
|
2010-09-02T14:21:05Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140726 |
| . |
| Reference:
|
[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. Zbl 0643.33001, MR 1225604 |
| Reference:
|
[2] Mecke J., Nagel W., Weiss V.: Length distributions of edges in planar stationary and isotropic STIT tessellations.J. Contemp. Math. Anal. 42 (2007), 28–43. Zbl 1155.60005, MR 2361580, 10.3103/S1068362307010025 |
| Reference:
|
[3] Mecke J., Nagel W., Weiss V.: Some distributions for I-segments of planar random homogeneous STIT tessellations.Math. Nachr. (2010)(to appear). MR 2832660 |
| Reference:
|
[4] Nagel W., Weiss V.: Crack STIT tessellations: characterization of stationary random tessellations stable with respect to iteration.Adv. in Appl. Probab. 37 (2005), 859–883. Zbl 1098.60012, MR 2193987, 10.1239/aap/1134587744 |
| Reference:
|
[5] Schneider R., Weil W.: Stochastic and Integral Geometry.Springer, Berlin, 2008. Zbl 1175.60003, MR 2455326 |
| Reference:
|
[6] Schreiber T., Thäle C.: Typical geometry, second-order properties and central limit theory for iteration stable tessellations.arXiv:1001.0990 [math.PR] (2010). MR 2796670 |
| Reference:
|
[7] Thäle C.: Moments of the length of line segments in homogeneous planar STIT tessellations.Image Anal. Stereol. 28 (2009), 69–76. MR 2538063, 10.5566/ias.v28.p69-76 |
| . |
