Maximizing the intersection density of fibre processes

Author:

Janson Svante,Kallenberg Olav

Abstract

It is shown that the specific intersection density of a stationary Poisson process of cylindrical fibres in Rd, d ≧ 2, attains its maximum when the directions are uniformly distributed. This generalizes a result by R. Davidson for line processes in R2.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Cited by 13 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. References;Stochastic Geometry and its Applications;2013-08-03

2. Stochastic and Integral Geometry;Probability and Its Applications;2008

3. Isoperimetric problems and roses of neighborhood for stationary flat processes;Mathematische Nachrichten;2003-03

4. A Duality for Poisson Flats;Advances in Applied Probability;1999-03

5. Zonoids and Generalisations;Handbook of Convex Geometry;1993

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