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Convergence to collinearity of a sequence of random triangle shapes

Published online by Cambridge University Press:  01 July 2016

David Mannion
David Mannion*
Affiliation:
Royal Holloway and Bedford New College
*
∗Postal address: Department of Mathematics, Royal Holloway and Bedford New College, Egham Hill, Egham, Surrey, TW200EX, UK.
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Abstract

A sequence of random triangles is constructed by choosing successively the three vertices of one triangle at random in the interior of its predecessor. A way is found to prove that the shapes of these triangles converge, almost surely, to collinear shapes, thus closing a gap in one of the central arguments of Mannion [5]. The new approach is based on a representation of the triangle process by a sequence of products of i.i.d. random matrices. We succeed in calculating the corresponding Lyapounov exponent.

Keywords

SHAPE-SPACESIMPLEXCONTENT OF SIMPLEXPRODUCTS OF RANDOM MATRICESLYAPOUNOV EXPONENT
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 4 , December 1990 , pp. 831 - 844
Copyright
Copyright © Applied Probability Trust 1990 

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References

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