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Poisson flats in Euclidean spaces Part I: A finite number of random uniform flats

Published online by Cambridge University Press:  01 July 2016

R. E. Miles
R. E. Miles*
Affiliation:
Australian National University
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Extract

This is the first part of a three part work, the common setting being Ed, Euclidean space of d dimensions. Many random physical phenomena, often in the form of structures, admit models which are assemblages of random s-flats in Ed. Indeed, taking s = 0, any n-sample from a d-dimensional distribution may of course be so regarded! For static phenomena generally 0 ≦ s < d ≦ 3, while 4 is to be substituted for 3 if time variation is allowed. By postulating a high degree of stochastic independence and uniformity, a variety of “simple” models is defined. However, their investigation poses problems in geometrical probability of a wide range of difficulty; the solutions of many of which are still far from complete.

Type
Research Article
Information
Advances in Applied Probability , Volume 1 , Issue 2 , Autumn 1969 , pp. 211 - 237
Copyright
Copyright © Applied Probability Trust 

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