Pith Number

pith:AKYAM3RV

pith:2026:AKYAM3RV4RDVPOSUUQ7T3HW3SB

not attested not anchored not stored refs resolved

The eigenvalues and eigenvectors of finite-rank normal perturbations of large rotationally invariant non-Hermitian matrices

Marc Potters, Pierre Bousseyroux

Finite-rank normal perturbations create outlier eigenvalues outside the bulk spectrum of large rotationally invariant non-Hermitian random matrices.

arxiv:2601.10427 v2 · 2026-01-15 · cond-mat.dis-nn · math-ph · math.MP · 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{AKYAM3RV4RDVPOSUUQ7T3HW3SB}

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 characterize the emergence and fluctuations of outlier eigenvalues in models of the form A + T, where A is a large rotationally invariant non-Hermitian random matrix and T is a finite-rank normal perturbation. We also describe the corresponding eigenvector behavior.

C2weakest assumption

The unperturbed matrix A must be rotationally invariant and the perturbation T must be normal and of finite rank; if either condition fails the outlier formulas no longer hold.

C3one line summary

Finite-rank normal perturbations of large rotationally invariant non-Hermitian random matrices produce outlier eigenvalues whose positions and fluctuations, together with the associated eigenvectors, are characterized in a unified framework that includes the Hermitian case.

References

20 extracted · 20 resolved · 0 Pith anchors

[1] Central limit theorems for eigenvalues in a spiked population model.Ann 2008

[2] Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices.Ann 2005

[3] Belinschi, Hari Bercovici, Mireille Capitaine, and Maxime F´ evrier 2017

[4] The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices.Advances in Mathematics, 227(1):494–521 2011

[5] Outliers in the single ring theorem.Probab 2016

Formal links

1 machine-checked theorem link

Cited by

3 papers in Pith

Spectral boundaries of deterministic matrices deformed by rotationally invariant random non-Hermitian ensembles

BBP transition and the leading eigenvector of the spiked Wigner model with inhomogeneous noise

Quantum many-body operator cascade as a route to chaos

Receipt and verification

First computed	2026-05-17T23:39:00.224937Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02b0066e35e44757ba54a43f3d9edb9074b61fa91cb80d34966c55d512479d41

Aliases

arxiv: 2601.10427 · arxiv_version: 2601.10427v2 · doi: 10.48550/arxiv.2601.10427 · pith_short_12: AKYAM3RV4RDV · pith_short_16: AKYAM3RV4RDVPOSU · pith_short_8: AKYAM3RV

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/AKYAM3RV4RDVPOSUUQ7T3HW3SB \
  | 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: 02b0066e35e44757ba54a43f3d9edb9074b61fa91cb80d34966c55d512479d41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7929bea63cb745c98fcf0b2fce2823a6467557c96c704721dbb9de3e3cda1cd",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2026-01-15T14:21:54Z",
    "title_canon_sha256": "dff6f98137e5fc265565180fe79089d8f2bebd1d1fde43cd232f79859f9ada49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.10427",
    "kind": "arxiv",
    "version": 2
  }
}