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Mixing Markov Chains and Their Images

Published online by Cambridge University Press:  27 July 2009

Michael F. Barnsley
Affiliation:
School of Mathematics Georgia Institute of Technology, Atlanta, Georgia 30332
Marc A. Berger
Affiliation:
Department of Theoretical MathematicsWeizmann Institute of Science, Rehovot 76100, Israel and Department of MathematicsCarnegie-Mellon University, Pittsburgh, Pennsylvania 15213
H. Meté Soner
Affiliation:
Department of MathematicsCarnegie-Mellon University, Pittsburgh, Pennsylvania 15213

Abstract

Recently, orbits of two-dimensional Markov chains have been used to generate computer images. These chains evolve according to products of i.i.d. affine maps. We deal with mixing models, whereby one mixes together several of these Markov chains, so as to create a mixed image. These mixtures involve starting one Markov chain off at the stationary distribution of another, and then running it for a geometrically distributed number of steps. We use this to analyze various mixing scenarios.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1988

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References

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