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Random cyclic transformations of points

Published online by Cambridge University Press:  14 July 2016

J. G. Veitch  and
G. S. Watson
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Abstract

We consider the action of independent and identically distributed n × n circulants S1, S2, … on V = [v1, …, vn] whose columns are the positions of n points in ℝd. The positions of the n points after m transformations are the columns of W(m) = VS1 … Sm. We describe, in several ways, the shape of the configuration of the points W(m) as m →∞. When n = 3, 4 and d = 2, a special discussion in terms of Moebius transformations is given.

Keywords

CIRCULANTSHAPESTOCHASTIC GEOMETRY
Type
Part 6—Allied Stochastic Processes
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 369 - 382
Copyright
Copyright © 1986 Applied Probability Trust 

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