Shapes of rectangular prisms after repeated random division

Shapes of rectangular prisms after repeated random division

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Article ID: iaor1998473
Country: United Kingdom
Volume: 29
Issue: 1
Start Page Number: 26
End Page Number: 37
Publication Date: Mar 1997
Journal: Advances in Applied Probability
Authors:
Keywords: markov processes
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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