Markov approximation of homogeneous lattice random fields

B. M. Gurevich, A. A. Tempelman

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We refine some well-known approximation theorems in the theory of homogeneous lattice random fields. In particular we prove that every translation invariant Borel probability measure μ on the space X of finite-alphabet configurations on ℤ can be weakly approximated by Markov measures μ n with supp(μ n )=X and with the entropies h(μ n )→h(μ). The proof is based on some facts of Thermodynamic Formalism; we also present an elementary constructive proof of a weaker version of this theorem.

Original languageEnglish (US)
Pages (from-to)519-527
Number of pages9
JournalProbability Theory and Related Fields
Issue number4
StatePublished - Apr 2005

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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