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

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- by Nishant Chandgotia, Guangyue Han, Brian Marcus, Tom Meyerovitch and Ronnie Pavlov PDF
- Proc. Amer. Math. Soc.
**142**(2014), 227-242 Request permission

## 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.## References

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## Additional Information

**Nishant Chandgotia**- Affiliation: Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada
- MR Author ID: 1040568
**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
- MR Author ID: 824249
**Ronnie Pavlov**- Affiliation: Department of Mathematics, University of Denver, Denver, Colorado 80208
- MR Author ID: 845553
- 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
- © Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3119198