Pith Number

pith:CSHQOOAG

pith:2026:CSHQOOAG662WBXD455JMTAVBU5

not attested not anchored not stored refs pending

On spectrum of sample correlation matrices from large fold tensor vectors

Wangjun Yuan

Sample correlation matrices from k-fold tensor vectors converge to the Marčenko-Pastur law when k grows slower than n.

arxiv:2604.06823 v2 · 2026-04-08 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CSHQOOAG662WBXD455JMTAVBU5}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Claims

C1strongest claim

we show that the limiting spectral distribution is the Marčenko-Pastur law. As a consequence, we show that the limiting spectral distribution of the Wishart matrix from the k-fold tensor product of independent uniformly distributed unit vectors in C^n is the Marčenko-Pastur law.

C2weakest assumption

The regime n, k → ∞ with k = o(n) together with the assumption that the base vectors have i.i.d. entries (or are uniformly distributed on the unit sphere) is sufficient for the tensor-structured sample matrices to inherit the Marchenko-Pastur limiting law.

C3one line summary

The limiting spectral distribution of sample correlation matrices from k-fold tensor vectors is the Marčenko-Pastur law when n, k → ∞ with k = o(n).

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-28T02:04:47.351851Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

148f073806f7b560dc7cef52c982a1a7496cc43a7d38c15e98891d24799b5f7c

Aliases

arxiv: 2604.06823 · arxiv_version: 2604.06823v2 · doi: 10.48550/arxiv.2604.06823 · pith_short_12: CSHQOOAG662W · pith_short_16: CSHQOOAG662WBXD4 · pith_short_8: CSHQOOAG

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/CSHQOOAG662WBXD455JMTAVBU5 \
  | 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: 148f073806f7b560dc7cef52c982a1a7496cc43a7d38c15e98891d24799b5f7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db000c9fb253578716ca683e4395f9970146e7677d5490c3bfd9f260b46794d4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-04-08T08:40:28Z",
    "title_canon_sha256": "0d5deb8bc729bcb99395630c881519fb6f8e3663c37273152f0e4a7cfe38fd78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.06823",
    "kind": "arxiv",
    "version": 2
  }
}