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The specific connectivity number of random networks

Part of: Geometric probability and stochastic geometry Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Joseph Mecke  and
Dietrich Stoyan
Joseph Mecke*
Affiliation:
University of Jena
Dietrich Stoyan*
Affiliation:
Freiberg University of Mining and Technology
*
∗ Postal address: Faculty of Mathematics and Informatics, University of Jena, 07740 Jena, Germany.
∗∗ Postal address: Institute of Stochastics, Freiberg University of Mining and Technology, 09596 Freiberg, Germany. Email address: [email protected]
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Abstract

A network is a system of segments or edges in ℝd which intersect only in the segment endpoints, which are called vertices. An example is the system of edges of a tessellation. It is possible to give formulas for the specific connectivity number of a random network; in the stationary case, the intensity of the 0-curvature measure is equal to the difference of the intensities of the point processes of vertices and edge centres.

Keywords

Euler characteristicgradientrandom networkspecific connectivity numbertessellation

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 62M30: Spatial processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 33 , Issue 3 , September 2001 , pp. 576 - 583
Copyright
Copyright © Applied Probability Trust 2001 

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