Pith Number

pith:YFKBD3CP

pith:2026:YFKBD3CPKJEL7JCJDAG7W3A4EF

not attested not anchored not stored refs resolved

Concentration Inequalities for Sample Cross-Covariances

Daniel Sanz-Alonso, Jiaheng Chen

Sub-Gaussian sample cross-covariances deviate from their mean in operator norm at a rate governed by the effective ranks of the marginal covariances.

arxiv:2605.16733 v1 · 2026-05-16 · math.PR · math.ST · stat.TH

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\pithnumber{YFKBD3CPKJEL7JCJDAG7W3A4EF}

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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

For sub-Gaussian random vectors, a high-probability operator-norm bound for the deviation of the sample cross-covariance matrix governed by the effective ranks of the two marginal covariance matrices; in the Gaussian case, a matching expectation lower bound allowing arbitrary correlation between the two random vectors.

C2weakest assumption

The two random vectors are sub-Gaussian (or jointly Gaussian), which supplies the tail and moment properties used to control the deviation of the sample cross-covariance in operator norm.

C3one line summary

Proves sharp operator-norm concentration and expectation bounds for sample cross-covariances of sub-Gaussian and Gaussian vectors, governed by effective ranks of the marginal covariances.

References

300 extracted · 300 resolved · 4 Pith anchors

[1] Ghattas, Omar Al and Bao, Jiajun and Sanz-Alonso, Daniel , journal=

[2] Majda, A. J. and Tong, X. T. , journal=. 2018 , publisher= 2018

[3] Tong, X. T. , journal=. 2018 , publisher= 2018

[4] Nonparametric estimation of large covariance matrices of longitudinal data , author=. Biometrika , volume=. 2003 , publisher= 2003

[5] Advances In Statistics , pages= 2008

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:02:38.922606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c15411ec4f5248bfa449180dfb6c1c2167bdb95a0700da63e5d713eaa73d81a4

Aliases

arxiv: 2605.16733 · arxiv_version: 2605.16733v1 · doi: 10.48550/arxiv.2605.16733 · pith_short_12: YFKBD3CPKJEL · pith_short_16: YFKBD3CPKJEL7JCJ · pith_short_8: YFKBD3CP

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YFKBD3CPKJEL7JCJDAG7W3A4EF \
  | 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: c15411ec4f5248bfa449180dfb6c1c2167bdb95a0700da63e5d713eaa73d81a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "137281ba770c67bb41bad533352187752afcdd22cd6c60844e6b112c91b8a50c",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-16T00:58:51Z",
    "title_canon_sha256": "8a55c7cc866c63fccaad65c949f84013bc2e0a95f1ee04e29e49d044d09c639e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16733",
    "kind": "arxiv",
    "version": 1
  }
}