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The invariant distribution of a sequence of random collinear 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, TW20 0EX, UK.
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Abstract

The shape of the nth in a sequence of random triangle shapes is (xn, yn). It was shown in [8] and [9] that yn → 0, almost surely, as n → ∞. In this paper we show that x„ converges in distribution, as n→∞, to a random variable x, and we find the probability distribution of x. The convergence in law of xn enables us to complete an argument used in one part of [9].

Keywords

RANDOM TRIANGLERANDOM TRIANGLE SHAPESHAPE THEORYRANDOM SIMPLEXES
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 4 , December 1990 , pp. 845 - 865
Copyright
Copyright © Applied Probability Trust 1990 

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