Markov approximation of homogeneous lattice random fields

• 成果类型: Article
• 署名作者: Gurevich, BM; Tempelman, AA
• 署名单位: Lomonosov Moscow State University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0383-6
• 发表日期: 2005
• 页码: 519-527
• 关键词: hausdorff dimension; generic points; gibbs measures; sets

摘要

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 mu on the space X of finite-alphabet configurations on Z(d), d >= 1, can be weakly approximated by Markov measures mu(n) with supp(mu(n)) = X and with the entropies h(mu(n)) --> h(mu). The proof is based on some facts of Thermodynamic Formalism; we also present an elementary constructive proof of a weaker version of this theorem.