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

Nishant Chandgotia, Guangyue Han, Brian Marcus, Tom Meyerovitch, Ronnie Pavlov

Research output: Contribution to journalArticlepeer-review


A topological Markov chain is the support of an ordinary firstorder 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.

Original languageAmerican English
Pages (from-to)227-242
Number of pages16
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - 1 Jan 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


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