Pith Number

pith:FWEIJ46H

pith:2003:FWEIJ46HUZMEUIILLR55RI4Q2R

not attested not anchored not stored refs pending

On the largest eigenvalue of Wishart matrices with identity covariance when n, p and p/n tend to infinity

Noureddine El Karoui

arxiv:math/0309355 v1 · 2003-09-22 · math.ST · stat.TH

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FWEIJ46HUZMEUIILLR55RI4Q2R}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Cited by

1 paper in Pith

Asymptotic Expansions of the Limit Laws of Gaussian and Laguerre (Wishart) Ensembles at the Soft Edge

Receipt and verification

First computed	2026-07-04T15:01:52.978620Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d8884f3c7a6584a210b5c7bd8a390d4639869978f51257f3aa1065eae476e2e

Aliases

arxiv: math/0309355 · arxiv_version: math/0309355v1 · doi: 10.48550/arxiv.math/0309355 · pith_short_12: FWEIJ46HUZME · pith_short_16: FWEIJ46HUZMEUIIL · pith_short_8: FWEIJ46H

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/FWEIJ46HUZMEUIILLR55RI4Q2R \
  | 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: 2d8884f3c7a6584a210b5c7bd8a390d4639869978f51257f3aa1065eae476e2e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "679724fe9e883da63d39197ce334dd72e4ac54314ea0e6835f3d6715b2aa773d",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "",
    "primary_cat": "math.ST",
    "submitted_at": "2003-09-22T08:36:06Z",
    "title_canon_sha256": "42bf0d72bbd0d1c0f867143ebc2c7edd67ddd8ed685dfe8329cf4b82b027f302"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0309355",
    "kind": "arxiv",
    "version": 1
  }
}