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August 2007 Limit theorems for functionals on the facets of stationary random tessellations
Lothar Heinrich, Hendrik Schmidt, Volker Schmidt
Bernoulli 13(3): 868-891 (August 2007). DOI: 10.3150/07-BEJ6131

Abstract

We observe stationary random tessellations X={Ξn}n≥1 in ℝd 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≤kd−1) by their intersections with the (d−1)-facets of independent and identically distributed motion-invariant tessellations Xn generated within each cell Ξn 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).

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Lothar Heinrich. Hendrik Schmidt. Volker Schmidt. "Limit theorems for functionals on the facets of stationary random tessellations." Bernoulli 13 (3) 868 - 891, August 2007. https://doi.org/10.3150/07-BEJ6131

Information

Published: August 2007
First available in Project Euclid: 7 August 2007

zbMATH: 1156.60010
MathSciNet: MR2348755
Digital Object Identifier: 10.3150/07-BEJ6131

Rights: Copyright © 2007 Bernoulli Society for Mathematical Statistics and Probability

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Vol.13 • No. 3 • August 2007
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