English

Birth-time distributions of weighted polytopes in STIT tessellations

Probability 2012-09-04 v1

Abstract

The lower-dimensional maximal polytopes associated with an iteration stable (STIT) tessellation in \RRd\RR^d are considered. They arise in the spatio-temporal construction process of such a tessellation as intersections of (d1)(d-1)-dimensional maximal polytopes. A precise description of the joint distribution of their birth-times is obtained. This in turn is used to determine the probabilities that the typical or the length-weighted typical maximal segment of the tessellation contains a fixed number of internal vertices.

Keywords

Cite

@article{arxiv.1209.0423,
  title  = {Birth-time distributions of weighted polytopes in STIT tessellations},
  author = {Nguyen Ngoc Linh and Christoph Thaele},
  journal= {arXiv preprint arXiv:1209.0423},
  year   = {2012}
}