The so-called STIT tessellations form a class of homogeneous (spatially
stationary) tessellations in Rd which are stable under
the nesting/iteration operation. In this paper we establish the mixing property
for these tessellations and give the decay rate of
P(A ∩ M = ∅, ThB ∩ M = ∅) /
P(A ∩ Y = ∅)P(B ∩ Y = ∅) - 1,
where A and B are both compact connected sets, h is a
vector of Rd, Th is the
corresponding translation operator, and M is a STIT tessellation.
Publié le : 2011-03-15
Classification:
Stochastic geometry,
random tessellation,
STIT tessellation,
space ergodicity,
mixing property,
60D05,
05B45,
37A25
@article{1300198511,
author = {Lachi\`eze-Rey, R.},
title = {Mixing properties for STIT tessellations},
journal = {Adv. in Appl. Probab.},
volume = {43},
number = {1},
year = {2011},
pages = { 40-48},
language = {en},
url = {http://dml.mathdoc.fr/item/1300198511}
}
Lachièze-Rey, R. Mixing properties for STIT tessellations. Adv. in Appl. Probab., Tome 43 (2011) no. 1, pp. 40-48. http://gdmltest.u-ga.fr/item/1300198511/