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A Duality for Poisson Flats

Part of: Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Rolf Schneider
Rolf Schneider*
Affiliation:
Albert-Ludwigs Universität, Freiburg
*
∗ Postal address: Mathematisches Institut, Albert-Ludwigs Universität, Eckerstr. 1, D 79104 Freiburg i Br, Germany. Email address: rschnei@ruf.uni-freiburg.de
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Abstract

In keeping with the intersection density of a stationary Poisson process of r-flats in Euclidean d-space, where r ≥ d/2, we introduce a notion of closeness, called proximity, for such processes if r < d/2. It is shown that the two notions are connected by a duality: the proximity of a stationary Poisson r-flat process is, up to a constant factor, the intersection density of a certain unique stationary Poisson (d − r)-flat process.

Keywords

Poisson flat processintersection density

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 31 , Issue 1 , March 1999 , pp. 63 - 68
Copyright
Copyright © Applied Probability Trust 1999 

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