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On point processes on the circle

Published online by Cambridge University Press:  14 July 2016

Jürg Hüsler
Jürg Hüsler*
Affiliation:
University of Berne
*
∗Postal address: Dept. of Mathematical Statistics, University of Berne, Sidlerstrasse 5, CH-3012 Berne, Switzerland.
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Abstract

Point processes on the circle with circumference 1 are considered, which are related to the coverage problem of the circle by n randomly placed arcs of a fixed length. The anticlockwise endpoint of each arc is assumed to be uniformly distributed on the circle. We deal with a general limit result on the convergence of these point processes to a Poisson process on the circle. This result is then applied to several cases of the coverage problem, giving improved limit results in these cases. The proof uses a new convergence result of general point processes.

Keywords

COVERAGEVACANCYEXTREME GAPSRANDOM ARCSCONVERGENCE
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 322 - 331
Copyright
Copyright © Applied Probability Trust 1986 

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