{"paper":{"title":"Large deviations for equilibrium measures and selection of subaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Jairo K. Mengue","submitted_at":"2016-08-21T00:32:03Z","abstract_excerpt":"Given a Lipschitz function $f:\\{1,...,d\\}^\\mathbb{N} \\to \\mathbb{R}$, for each $\\beta>0$ we denote by $\\mu_\\beta$ the equilibrium measure of $\\beta f$ and by $h_\\beta$ the main eigenfunction of the Ruelle Operator $L_{\\beta f}$. Assuming that $\\{\\mu_{\\beta}\\}_{\\beta>0}$ satisfy a large deviation principle, we prove the existence of the uniform limit $V= \\lim_{\\beta\\to\\infty}\\frac{1}{\\beta}\\log(h_{\\beta})$. Furthermore, the expression of the deviation function is determined by its values at the points of the union of the supports of maximizing measures. We study a class of potentials having two"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05881","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"}