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One-dimensional Markov random fields, Markov chains and topological Markov fields


Authors: Nishant Chandgotia, Guangyue Han, Brian Marcus, Tom Meyerovitch and Ronnie Pavlov
Journal: Proc. Amer. Math. Soc. 142 (2014), 227-242
MSC (2010): Primary 37-XX, 60-XX
DOI: https://doi.org/10.1090/S0002-9939-2013-11741-7
Published electronically: October 3, 2013
MathSciNet review: 3119198
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Abstract: A topological Markov chain is the support of an ordinary first-order Markov chain. We develop the concept of topological Markov field (TMF), which is the support of a Markov random field. Using this, we show that any one-dimensional (discrete-time, finite-alphabet) stationary Markov random field must be a stationary Markov chain, and we give a version of this result for continuous-time processes. We also give a general finite procedure for deciding if a given shift space is a TMF.


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Additional Information

Nishant Chandgotia
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

Guangyue Han
Affiliation: Department of Mathematics, The University of Hong Kong, Pok Fu Lam Road, Pokfulam, Hong Kong

Brian Marcus
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

Tom Meyerovitch
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada
Address at time of publication: Ben-Gurion University, P. O. Box 653, Be’er Sheva 84105, Israel

Ronnie Pavlov
Affiliation: Department of Mathematics, University of Denver, Denver, Colorado 80208

DOI: https://doi.org/10.1090/S0002-9939-2013-11741-7
Received by editor(s): December 18, 2011
Received by editor(s) in revised form: March 3, 2012
Published electronically: October 3, 2013
Communicated by: Bryna Kra
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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