Pith Number

pith:IC7FN3AO

pith:2026:IC7FN3AOU2JJTUVDKM5FT4DYV3

not attested not anchored not stored refs resolved

R-transforms for non-Hermitian matrices: a spherical integral approach

Marc Potters, Pierre Bousseyroux

R-transforms for non-Hermitian random matrices originate from a single scalar function of two variables.

arxiv:2601.09360 v2 · 2026-01-14 · cond-mat.dis-nn · math-ph · math.MP · math.PR

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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

We show that the R-transforms used in the non-Hermitian context in fact originate from a single scalar function of two variables.

C2weakest assumption

The replica method can be rigorously applied to establish the connection between non-Hermitian R-transforms and spherical integrals for general ensembles.

C3one line summary

R-transforms for non-Hermitian matrices derive from one scalar function of two variables via spherical integrals and the replica method.

References

55 extracted · 55 resolved · 1 Pith anchors

[1] A Fourier view on the R-transform and related asymptotics of spherical integrals.Journal of functional analysis, 222(2):435–490, 2005 2005

[2] Rectangular R-transform as the limit of rectangular spherical integrals 2011

[3] F. Haake, F. Izrailev, N. Lehmann, et al. Statistics of complex levels of random matrices for open quantum systems.Z. Phys. B, 88:359–370, 1992 1992

[4] Y. V. Fyodorov and H.-J. Sommers. Statistics of S-matrix poles in few-channel chaotic scattering. JETP Letters, 63:1026–1030, 1996 1996

[5] Y. V. Fyodorov and H.-J. Sommers. Statistics of resonance poles, phases, and time delays in quantum chaotic scattering.J. Math. Phys., 38:1918–1981, 1997 1918

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

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

Receipt and verification

First computed	2026-05-17T23:39:04.512200Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

40be56ec0ea69299d2a3533a59f078aee881135d17b3317199b5fa6a161e4360

Aliases

arxiv: 2601.09360 · arxiv_version: 2601.09360v2 · doi: 10.48550/arxiv.2601.09360 · pith_short_12: IC7FN3AOU2JJ · pith_short_16: IC7FN3AOU2JJTUVD · pith_short_8: IC7FN3AO

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/IC7FN3AOU2JJTUVDKM5FT4DYV3 \
  | 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: 40be56ec0ea69299d2a3533a59f078aee881135d17b3317199b5fa6a161e4360

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef5fdc3377dee91148fbbb76440a8357b5744ebddc8cc778f38ecb72b67e2539",
    "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": "2026-01-14T10:40:27Z",
    "title_canon_sha256": "666d36d03c0eddad6f8c3f71d7efee06602a35ea0d9f38ff470a9127d91c3731"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.09360",
    "kind": "arxiv",
    "version": 2
  }
}