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On the mean shape of particle processes

Part of: Stochastic processes General convexity Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Wolfgang Weil
Wolfgang Weil*
Affiliation:
Universität Karlsruhe
*
*Postal address: Mathematisches Institut II, Universität Karlsruhe, 76128 Karlsruhe, Germany.
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Abstract

For a stationary point process X of sets in the convex ring in ℝd, a relation is given between the mean particles of the section process X ∩ E (where E varies through the set of k-dimensional subspaces in ℝd) and a mean particle of X. In particular, it is shown that the mean bodies of all planar sections of X determine the Blaschke body of X and hence the mean normal distribution of X.

Keywords

PARTICLE PROCESSMEAN BODYBLASCHKE BODYSUPPORT FUNCTIONRANDOM SECTION

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes 52A10: Convex sets in $2$ dimensions (including convex curves)
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 29 , Issue 4 , December 1997 , pp. 890 - 908
Copyright
Copyright © Probability Trust 1997 

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