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A Markov chain of triangle shapes

Published online by Cambridge University Press:  01 July 2016

David Mannion
David Mannion*
Affiliation:
Royal Holloway and Bedford New College, London
*
∗Postal address: Department of Mathematics, Royal Holloway and Bedford New College, Egham Hill, Egham, Surrey TW20 OEX, UK.
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Abstract

The process of choosing a random triangle inside a compact convex region, K, may be iterated when K itself is a triangle. In this way successive generations of random triangles are created. Properties of scale, location and orientation are filtered out, leaving only the shapes of the triangles as the objects of study. Various simulation investigations indicate quite clearly that, as n increases, the nth-generation triangle shape converges to collinearity. In this paper we attempt to establish such convergence; our results fall slightly short of a complete proof.

Keywords

RANDOM TRIANGLESCOLLINEAR TRIANGLESRANDOM SHAPESSHAPE SPACESHAPE DISTRIBUTIONS: PRODUCTS OF RANDOM MATRICESLYAPUNOV EXPONENTS
Type
Research Article
Information
Advances in Applied Probability , Volume 20 , Issue 2 , June 1988 , pp. 348 - 370
Copyright
Copyright © Applied Probability Trust 1988 

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