{"paper":{"title":"A Large Deviation Principle for Gibbs States on Markov Shifts at Zero Temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Edgardo P\\'erez, Jairo K. Mengue, Rodrigo Bissacot","submitted_at":"2016-12-17T22:19:32Z","abstract_excerpt":"Let $\\Sigma_{A}(\\mathbb{N})$ be a topologically mixing countable Markov shift with the BIP property over the alphabet $\\mathbb{N}$ and $f: \\Sigma_{A}(\\mathbb{N}) \\rightarrow \\mathbb{R}$ a potential satisfying the Walters condition with finite Gurevich pressure. Under suitable hypotheses, we prove the existence of a Large Deviation Principle for the family $(\\mu_{\\beta})_{\\beta > 0}$ where each $\\mu_{\\beta}$ is the Gibbs measure associated to the potential $\\beta f$. Our main theorem generalizes from finite to countable alphabets and also to a larger class of potentials a previous result of A. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05831","kind":"arxiv","version":2},"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"}