{"paper":{"title":"Large Deviations for stationary probabilities of a family of continuous time Markov chains via Aubry-Mather theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.PR"],"primary_cat":"math.DS","authors_text":"Adriana Neumann, Artur O. Lopes","submitted_at":"2014-02-04T17:50:56Z","abstract_excerpt":"We consider a family of continuous time symmetric random walks indexed by $k\\in \\mathbb{N}$, $\\{X_k(t),\\,t\\geq 0\\}$. For each $k\\in \\mathbb{N}$ the matching random walk take values in the finite set of states $\\Gamma_k=\\frac{1}{k}(\\mathbb{Z}/k\\mathbb{Z})$ which is a subset of the unitary circle. The stationary probability for such process converges to the uniform distribution on the circle, when $k\\to \\infty$.\n  We disturb the system considering a fixed $C^2$ potential $V: \\mathbb{S}^1 \\to \\mathbb{R}$ and we will denote by $V_k$ the restriction of $V$ to $\\Gamma_k$. Then, we define a non-stoch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0809","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"}