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Maximizing the intersection density of fibre processes

Published online by Cambridge University Press:  14 July 2016

Svante Janson  and
Olav Kallenberg
Svante Janson*
Affiliation:
Uppsala University
Olav Kallenberg*
Affiliation:
Göteborg University
*
∗Postal address: Uppsala University, Department of Mathematics, Thunbergsvägen 3, S-752 38 Uppsala, Sweden.
∗∗Postal address: Mathematics Department, Chalmers University of Technology, S-412 96 Göteborg, Sweden.
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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.

Keywords

STATIONARY LINE PROCESSESINTERSECTION DENSITYUNIFORM DISTRIBUTION OF DIRECTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 820 - 828
Copyright
Copyright © Applied Probability Trust 1981 

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Footnotes

Research partly done at the Mittag-Leffler Institute.

References

[1] Erdélyi, A., (Ed.) (1953) Higher Transcendental Functions II. McGraw-Hill, New York.Google Scholar
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[4] Stein, E. M. and Weiss, G. (1971) Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press.Google Scholar
[5] Szegö, G. (1959) Orthogonal Polynomials , 2nd edn. A.M.S. Colloquium Publ. 23, New York.Google Scholar