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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1402.0809","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-02-04T17:50:56Z","cross_cats_sorted":["cond-mat.stat-mech","math.PR"],"title_canon_sha256":"30d6a308c639ce0c5d18490a21fb09d3f78ab7bba7c373d4ebf8a71bcebd4e9c","abstract_canon_sha256":"7864fc7ad97cb8655af1866e750f2bb116945b40c7d1126e9edd69212e9f4080"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:47.880511Z","signature_b64":"0iS3xEBTkrW8U3WDBwZ56JXO+VJeHrHO6QOS2W0mXm3upOLsiRkSaXMU50iqjGBzfyiQ4AdurIC3Hnh2vRj+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5c20f1cdbf34a00e4b5f074f07e661f6e24c90cc383a0f229a65fad19bd98a3","last_reissued_at":"2026-05-18T01:44:47.879827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:47.879827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\Gamma_k$. 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