| Affiliation: | (1) Leninskie Gory, Department of Mechanics and Mathematics, Moscow State University, 119992 Moscow, Russia;(2) Department of Statistics, Penn State University, 325 Thomas Bldg., University Park, PA 16802, USA |
| Abstract: | 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  on the space X of finite-alphabet configurations on  d, d 1, can be weakly approximated by Markov measures n with supp(n)=X and with the entropies h(n) h(). The proof is based on some facts of Thermodynamic Formalism; we also present an elementary constructive proof of a weaker version of this theorem.Mathematics Subject Classifications (2000): Primary 28D20, 37C85, 60G60; secondary 82B20Dedicated to Professor A. I. Vorobyov, member of the Russian Academy of Sciences and Director of the Hematology Research Center of the Russian Academy of Medical Sciences, on the occasion of his 75th birthday |
