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 are considered. They arise in the spatio-temporal construction process of such a tessellation as intersections of -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}
}