Pith Number

pith:U5DD3PKF

pith:2026:U5DD3PKFOPAKMRHZ43XRFWMA7D

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

Marc Potters, Pierre Bousseyroux

The complex eigenvalues of a deterministic matrix plus a rotationally invariant random matrix lie inside boundaries given by simple equations from the R1 and R2 transforms of the random matrix.

arxiv:2602.16878 v2 · 2026-02-18 · cond-mat.dis-nn · math-ph · math.MP · math.PR

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\pithnumber{U5DD3PKFOPAKMRHZ43XRFWMA7D}

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4 Citations 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

In the large-N limit, we show that the complex eigenvalue distribution of A + B satisfies remarkably simple boundary equations that depend on the R1 and R2 transforms of B.

C2weakest assumption

That B belongs to a rotationally invariant ensemble so that its statistics are fully captured by the R1 and R2 transforms in the complex plane.

C3one line summary

Spectral boundaries of A + B (A deterministic, B rotationally invariant random non-Hermitian) are given by simple equations depending on the R1 and R2 transforms of B in the large-N limit.

References

30 extracted · 30 resolved · 3 Pith anchors

[1] The Brown measure of a sum of two free random variables, one of which is R-diagonal.arXiv preprint arXiv:2209.12379, 2022 2022

[2] Computation of some examples of Brown's spectral measure in free probability 1999 · arXiv:math/9912242

[3] Computation of some examples of Brown’s spectral measure in free probability.Colloquium Mathematicae, 90(2):181–211, 2001 2001

[4] The eigenvalues and eigenvectors of finite-rank normal perturbations of large rotationally invariant non-Hermitian matrices 2026 · arXiv:2601.10427

[5] R-transforms for non-Hermitian matrices: a spherical integral approach 2026 · arXiv:2601.09360

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:38:59.925497Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7463dbd4573c0a644f9e6ef12d980f8e0f51fe3fd625390f07f2a4400fc4350

Aliases

arxiv: 2602.16878 · arxiv_version: 2602.16878v2 · doi: 10.48550/arxiv.2602.16878 · pith_short_12: U5DD3PKFOPAK · pith_short_16: U5DD3PKFOPAKMRHZ · pith_short_8: U5DD3PKF

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/U5DD3PKFOPAKMRHZ43XRFWMA7D \
  | 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: a7463dbd4573c0a644f9e6ef12d980f8e0f51fe3fd625390f07f2a4400fc4350

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97c71dfd486d5a0cc47d344ed7ba35b000f0286d28bd5418898f75c9eb5cc04e",
    "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": "2026-02-18T21:02:02Z",
    "title_canon_sha256": "423a6f453cc1a131f282699dc782cf289cc8787b3174f00f9a481bb1e58cd93b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.16878",
    "kind": "arxiv",
    "version": 2
  }
}