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On the mean shape of particle processes

Published online by Cambridge University Press:  01 July 2016

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

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 XE (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.

Type
Stochastic Geometry and Statistical Applications
Copyright
Copyright © Probability Trust 1997 

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