Hostname: page-component-7f64f4797f-8cpv7 Total loading time: 0 Render date: 2025-11-04T08:02:42.808Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

Abstract

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

Keywords

STATIONARY LINE PROCESSESINTERSECTION DENSITYUNIFORM DISTRIBUTION OF DIRECTIONS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 820 - 828
Copyright
Copyright © Applied Probability Trust 1981 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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
[2] Harding, E. F. and Kendall, D. G., (Eds.) (1974) Stochastic Geometry. Wiley, New York.Google Scholar
[3] Kallenberg, O. (1976–81) On the structure of stationary flat processes I–III. Z. Wahrscheinlichkeitsth. 37, 157–174; 52, 127–147; 56, 239–253.CrossRefGoogle Scholar
[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