{"paper":{"title":"Approximating entropy for a class of $\\zz^2$ Markov Random Fields and pressure for a class of functions on $\\zz^2$ shifts of finite type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Brian Marcus, Ronnie Pavlov","submitted_at":"2010-09-15T23:36:38Z","abstract_excerpt":"For a class of $\\zz^2$ Markov Random Fields (MRFs) $\\mu$, we show that the sequence of successive differences of entropies of induced MRFs on strips of height $n$ converges exponentially fast (in $n$) to the entropy of $\\mu$. These strip entropies can be computed explicitly when $\\mu$ is a Gibbs state given by a nearest-neighbor interaction on a strongly irreducible nearest-neighbor $\\zz^2$ shift of finite type $X$. We state this result in terms of approximations to the (topological) pressures of certain functions on such an $X$, and we show that these pressures are computable if the values ta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3063","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}