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Shapes of Rectangular Prisms After Repeated Random Division

Part of: Distribution theory - Probability Markov processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Richard Cowan
Richard Cowan*
Affiliation:
University of Hong Kong
*
∗ Postal address: Department of Statistics, University of Hong Kong, Pokfulam Road, Hong Kong. Email: [email protected]
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Abstract

The shape of a rectangular prism in (d + 1)-dimensions is defined as Y = (Y1, Y2, · ··, Yd), Yn = Ln/Ln+1 where the Ln are the prism's edge lengths, in ascending order. We investigate shape distributions that are invariant when the prism is cut into two, also rectangular, prisms, with one prism retained for measurement and the other discarded. Interesting new distributions on [0, 1]d arise.

Keywords

INVARIANT DISTRIBUTIONSSHAPE DISTRIBUTIONSRANDOM GEOMETRYDISTRIBUTION THEORYMARKOV PROCESSES

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60E05: Distributions 60J05: Discrete-time Markov processes on general state spaces
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 29 , Issue 1 , March 1997 , pp. 26 - 37
Copyright
Copyright © Applied Probability Trust 1997 

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