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pith:DKVOFITT

pith:2023:DKVOFITTCTW4HMMUJBZTAJYR46

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Eigenvalues, eigenvector-overlaps, and regularized Fuglede-Kadison determinant of the non-Hermitian matrix-valued Brownian motion

Makoto Katori, Satoshi Yabuoku, Syota Esaki

Non-Hermitian matrix Brownian motion admits scale-invariant SDEs coupling eigenvalues to eigenvector overlaps via a regularized Fuglede-Kadison determinant.

arxiv:2306.00300 v4 · 2023-06-01 · math.PR · cond-mat.stat-mech · math-ph · math.MP

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\pithnumber{DKVOFITTCTW4HMMUJBZTAJYR46}

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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 derive a set of stochastic differential equations (SDEs) for the coupled system of the eigenvalue process and the eigenvector-overlap process and prove the scale-transformation invariance of the obtained SDE system.

C2weakest assumption

The bi-orthogonality relation is imposed between the right and the left eigenvector processes, which allows for their scale transformations with an invariant eigenvalue process.

C3one line summary

Derives coupled SDEs for eigenvalue and eigenvector-overlap processes in non-Hermitian Brownian motion and SPDEs for the regularized FK determinant random field.

References

42 extracted · 42 resolved · 0 Pith anchors

[1] Random Ma trices: Theory and Applications 9 (4), 2050015 (2000) 2000

[2] D.: Circular law 1997

[3] A., Speicher, R., Tarnowski, W.: Squared eig envalue condition numbers and eigenvector correlations from the single ring theorem 2017

[4] T., ´Sniady, P., Speicher, R.: Eigenvalues of non-Hermitian random matric es and Brown measure of non-normal operators: Hermitian reductio n and linearization method 2018

[5] R.: The Cauchy Transform, Potential Theory and Confor mal Mapping 2016

Receipt and verification

First computed	2026-06-23T02:13:11.770464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1aaae2a27314edc3b1944873302711e79ad4e6ebfc83a33c2f2b876758658ae2

Aliases

arxiv: 2306.00300 · arxiv_version: 2306.00300v4 · doi: 10.48550/arxiv.2306.00300 · pith_short_12: DKVOFITTCTW4 · pith_short_16: DKVOFITTCTW4HMMU · pith_short_8: DKVOFITT

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DKVOFITTCTW4HMMUJBZTAJYR46 \
  | 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: 1aaae2a27314edc3b1944873302711e79ad4e6ebfc83a33c2f2b876758658ae2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "570e437a870a390d5acee413127b1c943e1712d0db23f697e912355e8f439ef8",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2023-06-01T02:39:19Z",
    "title_canon_sha256": "7a4a30ea6e103e9b31246706640c5bbf8788e605bfa6f08f5a0c36fba214e2e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2306.00300",
    "kind": "arxiv",
    "version": 4
  }
}