Intrinsic Volumes of the Maximal Polytope Process in Higher Dimensional STIT Tessellations

Details Intrinsic Volumes of the Maximal Polytope Process in Higher Dimensional STIT Tessellations Intrinsic Volumes of the Maximal Polytope Process in Higher Dimensional STIT Tessellations

2010-06-28

arxiv.org/abs/1006.5338v2

Stoch. Proc. Appl. 121, pages 989-1012 (2011)

Mathematics

Probability

27 pages

Scientific paper

Stationary and isotropic iteration stable random tessellations are considered, which can be constructed by a random process of cell division. The collection of maximal polytopes at a fixed time $t$ within a convex window $W\subset{\Bbb R}^d$ is regarded and formulas for mean values, variances, as well as a characterization of certain covariance measures are proved. The focus is on the case $d\geq 3$, which is different from the planar one, treated separately in \cite{ST2}. Moreover, a multivariate limit theorem for the vector of suitably rescaled intrinsic volumes is established, leading in each component -- in sharp contrast to the situation in the plane -- to a non-Gaussian limit.

Affiliated with

Also associated with

No associations

Rating

Intrinsic Volumes of the Maximal Polytope Process in Higher Dimensional STIT Tessellations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Intrinsic Volumes of the Maximal Polytope Process in Higher Dimensional STIT Tessellations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Intrinsic Volumes of the Maximal Polytope Process in Higher Dimensional STIT Tessellations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-617006