Pith Number

pith:WTMBOUK6

pith:2026:WTMBOUK6N2CU3YMQRVZM7EAUJA

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Statistical Limit Theorems for Axiom A Diffeomorphisms: Exponential Mixing, Central Limit Theorem, and Large Deviations

Abdoulaye Thiam

The spectral gap of the Ruelle transfer operator implies five statistical limit theorems for Axiom A diffeomorphisms.

arxiv:2604.18930 v3 · 2026-04-21 · math.DS · math-ph · math.MP · math.PR

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

Cited by

6 papers in Pith

Transfer Operators and SRB Measures for Axiom A Diffeomorphisms: Spectral Gap, Structural Stability, and the Gibbs Equivalence Theorem

Multifractal Analysis, Liv\v{s}ic Rigidity, and Fluctuation Theorems for Axiom A Diffeomorphisms: The Pesin Formula and the Gallavotti-Cohen Symmetry

Transfer Operators and SRB Measures for Axiom A Diffeomorphisms: Spectral Gap, Structural Stability, and the Gibbs Equivalence Theorem

Uniform Hyperbolicity and Symbolic Dynamics: Markov Partitions, Shadowing, and the Coding of Axiom A Diffeomorphisms

Gibbs Measures on Subshifts of Finite Type: Five Equivalent Characterizations with Explicit Constants

Receipt and verification

First computed	2026-05-20T00:05:45.037904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4d817515e6e854de1908d72cf9014481380e8198fbfd8b5d996bae697228967

Aliases

arxiv: 2604.18930 · arxiv_version: 2604.18930v3 · doi: 10.48550/arxiv.2604.18930 · pith_short_12: WTMBOUK6N2CU · pith_short_16: WTMBOUK6N2CU3YMQ · pith_short_8: WTMBOUK6

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WTMBOUK6N2CU3YMQRVZM7EAUJA \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b4d817515e6e854de1908d72cf9014481380e8198fbfd8b5d996bae697228967

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "642412babb1bdf5b9fe6f898d936f210cd76f288a539b1e446dee071a91390f3",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-04-21T00:08:57Z",
    "title_canon_sha256": "1057a08301fb0a8b1fb8b17311de2dc1b00f1ed4277015c071697250670acd06"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.18930",
    "kind": "arxiv",
    "version": 3
  }
}