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The asymptotic distribution of random molecules

Published online by Cambridge University Press:  01 July 2016

Wulf Rehder
Wulf Rehder*
Affiliation:
Technische Universitat Berlin
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Abstract

If n solid spheres K n of some volume V(K n ) are scattered randomly in the unit cube of euclidean d-space, some of them will overlap to form L n (s) molecules with exactly s atoms K n. The random variable L n(s) has a limit distribution if V(K n ) tends to zero but nV(Kn ) tends to infinity at a certain rate: it is shown that for

L n(s) is asymptotically Poisson.

Keywords

POISSON PROCESSLIMIT THEOREMRANDOM CONVEX SETSFACTORIAL MOMENTS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 3 , September 1980, pp. 640 - 654
Copyright
Copyright © Applied Probability Trust 1980 

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