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On random divisions of a convex set
Published online by Cambridge University Press: 14 July 2016
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.
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- Copyright © Applied Probability Trust 1978
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