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Diffusion out of a triangle

Published online by Cambridge University Press:  14 July 2016

W. Smith  and
G. S. Watson
W. Smith
Affiliation:
The Johns Hopkins University
G. S. Watson
Affiliation:
The Johns Hopkins University
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Abstract

A problem in molecular genetics called for the following result. If a particle is dropped at random on a right-angled isosceles triangle, and thus allowed to execute symmetrical Brownian motion, the chance that it will first leave the triangle via the hypotenuse is 0.41062. An inequality and two methods of deriving this probability are illustrated. The most useful source of solutions to diffusion problems of this kind is the torsion problem of elasticity.

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 3 , November 1967 , pp. 479 - 488
Copyright
Copyright © Applied Probability Trust 

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