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On random divisions of a convex set

Published online by Cambridge University Press:  14 July 2016

Svante Janson
Svante Janson*
Affiliation:
Uppsala University
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Abstract

This paper gives an elementary proof that, under some general assumptions, the number of parts a convex set in Rd is divided into by a set of independent identically distributed hyperplanes is asymptotically normally distributed. An example is given where the distribution of hyperplanes is ‘too singular' to satisfy the assumptions, and where a different limiting distribution appears.

Keywords

GEOMETRICAL PROBABILITYRANDOM DIVISIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 645 - 649
Copyright
Copyright © Applied Probability Trust 1978 

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References

[1] Kendall, M. G. and Moran, P. A. P. (1963) Geometrical Probability. Griffin, London.Google Scholar
[2] Lomnicki, Z. A. and Zaremba, S. K. (1957) A further instance of the central limit theorem for dependent random variables. Math. Z. 66, 490–494.Google Scholar
[3] Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, New York.Google Scholar
[4] Miles, R. E. (1969), (1971) Poisson flats in Euclidean spaces, I, II. Adv. Appl. Prob. 1, 211–237; 3, 1–43.CrossRefGoogle Scholar
[5] Miles, R. E. (1973) The various aggregates of random polygons determined by random lines in a plane. Adv. Math. 10, 256–290.Google Scholar