Limit theorems for functionals on the facets of stationary random tessellations

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dc.creatorHeinrich, Lothar
dc.creatorSchmidt, Hendrik
dc.creatorSchmidt, Volker
dc.date2007-09-05
dc.date.accessioned2026-07-07T08:28:59Z
dc.date.available2026-07-07T08:28:59Z
dc.descriptionWe observe stationary random tessellations $X=\{Ξ_n\}_{n\ge1}$ in $\mathbb{R}^d$ through a convex sampling window $W$ that expands unboundedly and we determine the total $(k-1)$-volume of those $(k-1)$-dimensional manifold processes which are induced on the $k$-facets of $X$ ($1\le k\le d-1$) by their intersections with the $(d-1)$-facets of independent and identically distributed motion-invariant tessellations $X_n$ generated within each cell $Ξ_n$ of $X$. The cases of $X$ being either a Poisson hyperplane tessellation or a random tessellation with weak dependences are treated separately. In both cases, however, we obtain that all of the total volumes measured in $W$ are approximately normally distributed when $W$ is sufficiently large. Structural formulae for mean values and asymptotic variances are derived and explicit numerical values are given for planar Poisson--Voronoi tessellations (PVTs) and Poisson line tessellations (PLTs).
dc.descriptionPublished at http://dx.doi.org/10.3150/07-BEJ6131 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
dc.identifierhttps://arxiv.org/abs/0709.0650
dc.identifierhttp://arxiv.org/abs/0709.0650
dc.identifierBernoulli 2007, Vol. 13, No. 3, 868-891
dc.identifierdoi:10.3150/07-BEJ6131
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137809
dc.subjectProbability
dc.titleLimit theorems for functionals on the facets of stationary random tessellations
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