On the random coverage of the circle
- 1 September 1984
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 21 (3) , 558-566
- https://doi.org/10.2307/3213617
Abstract
Place n arcs of equal length a uniformly at random on the circumference of a circle. We discuss the joint limit distributions of the number of gaps, the uncovered proportion of the circle and the lengths of the largest gap and of the smallest gap, depending on how a → 0 as n →∞.We show that the results may be proved in a unified and simple way by using a result of Le Cam.Keywords
This publication has 15 references indexed in Scilit:
- Random coverage of the circle and asymptotic distributionsJournal of Applied Probability, 1982
- On Convergence of the Coverage by Random Arcs on a Circle and the Largest SpacingThe Annals of Probability, 1981
- On the lengths of the pieces of a stick broken at randomJournal of Applied Probability, 1980
- On multiple covering of a circle with random arcsJournal of Applied Probability, 1980
- Asymptotic Coverage Distributions on the CircleThe Annals of Probability, 1979
- Random arcs on the circleJournal of Applied Probability, 1978
- A limit theorem for random coverings of a circle which do not quite coverJournal of Applied Probability, 1978
- Two Applications of a Poisson Approximation for Dependent EventsThe Annals of Probability, 1977
- On a Class of Problems Related to the Random Division of an IntervalThe Annals of Mathematical Statistics, 1953
- SOLUTION TO A GEOMETRICAL PROBLEM IN PROBABILITYAnnals of Eugenics, 1939