The Annals of Probability

Random Cell Complexes and Generalised Sets

M. Zahle

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Abstract

The concept of random cell complexes, generalised sets and their mean sets in $R^d$ are introduced. Under stationarity conditions various relations between associated geometrical quantities are derived.

Article information

Source
Ann. Probab., Volume 16, Number 4 (1988), 1742-1766.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991595

Digital Object Identifier
doi:10.1214/aop/1176991595

Mathematical Reviews number (MathSciNet)
MR958214

Zentralblatt MATH identifier
0656.60024

JSTOR
links.jstor.org

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60G55: Point processes 58A25: Currents [See also 32C30, 53C65]

Keywords
Random cell complexes stationary point processes $i$-skeletons typical $j$-cells currents generalised sets mean sets curvature and direction properties polyhedron theorems random tessellations

Citation

Zahle, M. Random Cell Complexes and Generalised Sets. Ann. Probab. 16 (1988), no. 4, 1742--1766. doi:10.1214/aop/1176991595. https://projecteuclid.org/euclid.aop/1176991595


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