Pith Number

pith:SBKV3F3D

pith:2024:SBKV3F3DVKCEMRKQPKWFIW3YRL

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Precise large deviations through a uniform Tauberian theorem

Gaia Pozzoli, Giampaolo Cristadoro

A uniform Tauberian theorem for Laplace-Stieltjes transforms establishes large deviation principles for random variables attracted to spectrally positive stable distributions.

arxiv:2407.04059 v3 · 2024-07-04 · math.PR · math-ph · math.MP

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms.

C2weakest assumption

The random variables belong to the basin of attraction of spectrally positive stable distributions and satisfy the conditions under which the uniform Tauberian theorem applies, including regular variation.

C3one line summary

Establishes a uniform Tauberian theorem yielding precise large deviation principles for stable attraction basins, covering long-memory walks and infinite-mean stopping times.

References

69 extracted · 69 resolved · 0 Pith anchors

[1] Aleˇ skeviˇ cien´ e, R 2008

[2] R. Artuso, G. Cristadoro, M. Degli Esposti, and G. Knight. Spar re–Andersen theorem with spatiotemporal correlations. Phys. Rev. E , 89:052111, 2014 2014

[3] A. Bianchi, G. Cristadoro, and G. Pozzoli. Ladder costs for rand om walks in L´ evy random media. Stoch. Process. Their Appl. , 188:104666, 2025 2025

[4] N. H. Bingham. Tauberian theorems and large deviations. Stochastics, 80:143–149, 2008 2008

[5] N. H. Bingham, C. M. Goldie, and J. L. Teugels. Regular Variation. Cambridge University Press, Cambridge, 1987 1987

Receipt and verification

First computed	2026-05-25T02:01:01.099184Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90555d9763aa844645507aac545b788ac9875ce2f24d3892c16e4870ce1e4d29

Aliases

arxiv: 2407.04059 · arxiv_version: 2407.04059v3 · doi: 10.48550/arxiv.2407.04059 · pith_short_12: SBKV3F3DVKCE · pith_short_16: SBKV3F3DVKCEMRKQ · pith_short_8: SBKV3F3D

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SBKV3F3DVKCEMRKQPKWFIW3YRL \
  | 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: 90555d9763aa844645507aac545b788ac9875ce2f24d3892c16e4870ce1e4d29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "01b4a7da5cdf44abc6c6ed6ed49561b2b77f8178f1be1ec329f8e2e4f611af06",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-07-04T17:01:12Z",
    "title_canon_sha256": "522c2aa44986c5f2bf9b5dc539a93e00ccf81150fcca935c24e13679b5593ccf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.04059",
    "kind": "arxiv",
    "version": 3
  }
}