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Shapes of Rectangular Prisms After Repeated Random Division
Published online by Cambridge University Press: 01 July 2016
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.
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- Stochastic Geometry and Statistical Applications
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- Copyright © Applied Probability Trust 1997
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