{"paper":{"title":"Statistical Limit Theorems for Axiom A Diffeomorphisms: Exponential Mixing, Central Limit Theorem, and Large Deviations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The spectral gap of the Ruelle transfer operator implies five statistical limit theorems for Axiom A diffeomorphisms.","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.DS","authors_text":"Abdoulaye Thiam","submitted_at":"2026-04-21T00:08:57Z","abstract_excerpt":"We establish statistical limit theorems for equilibrium states of Axiom A diffeomorphisms, derived from the spectral gap of the Ruelle transfer operator established in Part I (Thiam2026a) and transferred to smooth dynamics through the Markov partition coding of Part III (Thiam2026c). This Part contains five Main Theorems. The first proves the Volume Lemma with explicit two-sided bounds on the Riemannian volume of dynamical Bowen balls in terms of Birkhoff sums of the geometric potential. The second establishes exponential decay of correlations with explicit mixing rates computed from the spect"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The five Main Theorems (Volume Lemma with two-sided volume bounds, exponential decay of correlations with explicit rates, CLT with optimal Berry-Esseen bounds and explicit variance formula, ASIP with polynomial error, and LDP with rate function the Legendre transform of the pressure) all follow from the spectral gap of the normalized transfer operator transferred through Markov partition coding.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The spectral gap of the Ruelle transfer operator established in Part I (Thiam2026a) together with the Markov partition coding of Part III (Thiam2026c) that allows the gap to be transferred to the original smooth dynamics.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Derives the Volume Lemma, exponential mixing, CLT with Berry-Esseen bounds, ASIP, and LDP for Axiom A diffeomorphisms from the spectral gap of the normalized Ruelle transfer operator with explicit hyperbolicity dependence.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The spectral gap of the Ruelle transfer operator implies five statistical limit theorems for Axiom A diffeomorphisms.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ad21e27ae4573af75b49bb0c17ca5fa5bb87f96496ef79bdd7094e3db365ffe6"},"source":{"id":"2604.18930","kind":"arxiv","version":3},"verdict":{"id":"2582a38f-8368-4bc6-84d1-1b4e42454cd2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T02:12:20.794387Z","strongest_claim":"The five Main Theorems (Volume Lemma with two-sided volume bounds, exponential decay of correlations with explicit rates, CLT with optimal Berry-Esseen bounds and explicit variance formula, ASIP with polynomial error, and LDP with rate function the Legendre transform of the pressure) all follow from the spectral gap of the normalized transfer operator transferred through Markov partition coding.","one_line_summary":"Derives the Volume Lemma, exponential mixing, CLT with Berry-Esseen bounds, ASIP, and LDP for Axiom A diffeomorphisms from the spectral gap of the normalized Ruelle transfer operator with explicit hyperbolicity dependence.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The spectral gap of the Ruelle transfer operator established in Part I (Thiam2026a) together with the Markov partition coding of Part III (Thiam2026c) that allows the gap to be transferred to the original smooth dynamics.","pith_extraction_headline":"The spectral gap of the Ruelle transfer operator implies five statistical limit theorems for Axiom A diffeomorphisms."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.18930/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}