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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
8 articles.
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1. Poisson Point Process Convergence and Extreme Values in Stochastic Geometry;Stochastic Analysis for Poisson Point Processes;2016
2. Introduction to Stochastic Geometry;Stochastic Analysis for Poisson Point Processes;2016
3. Intersection and proximity of processes of flats;Journal of Mathematical Analysis and Applications;2015-06
4. Distances Between Poisson k -Flats;Methodology and Computing in Applied Probability;2013-01-30
5. The scaling limit of Poisson-driven order statistics with applications in geometric probability;Stochastic Processes and their Applications;2012-12