Pith Number

pith:LVQGTK5I

pith:2026:LVQGTK5IQ4QA4TH53EOEMWEVLP

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Mesoscopic Rates of Convergence for Complex Wishart Matrices at the Leftmost Spectrum Edge

Mengchun Cai

Laguerre unitary ensemble eigenvalues converge to the Airy process at mesoscopic scales in L1-Wasserstein distance at the left edge

arxiv:2605.12777 v1 · 2026-05-12 · math.PR

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Claims

C1strongest claim

We prove convergence rates at the leftmost edge of the LUE spectrum in the L1-Wasserstein distance for mesoscopic scales as dimension goes to infinity.

C2weakest assumption

The assumption that standard edge universality and determinantal structure for the Laguerre Unitary Ensemble hold uniformly under the mesoscopic scaling regime, allowing direct comparison of point counts.

C3one line summary

Mesoscopic L1-Wasserstein convergence rates are established for the left-edge eigenvalues of the Laguerre Unitary Ensemble to the Airy point process.

References

29 extracted · 29 resolved · 0 Pith anchors

[1] Oxford University Press, 1 edition, September 2015 2015

[2] Anderson, Alice Guionnet, and Ofer Zeitouni.An introduction to random matrices 2010

[3] Szarek.Alice and Bob meet Banach: the interface of asymptotic geometric analysis and quantum information theory 2017

[4] Z. D. Bai. Convergence rate of expected spectral distributions of large random matrices. part i. wigner matrices.The Annals of Probability, 21(2):625–648, 1993 1993

[5] Bai.Spectral analysis of large dimensional random matrices 2010

Receipt and verification

First computed	2026-05-18T03:09:13.201813Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d6069aba887200e4cfdd91c4658955bfd002cad65d66d09875959545c1334cb

Aliases

arxiv: 2605.12777 · arxiv_version: 2605.12777v1 · doi: 10.48550/arxiv.2605.12777 · pith_short_12: LVQGTK5IQ4QA · pith_short_16: LVQGTK5IQ4QA4TH5 · pith_short_8: LVQGTK5I

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LVQGTK5IQ4QA4TH53EOEMWEVLP \
  | 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: 5d6069aba887200e4cfdd91c4658955bfd002cad65d66d09875959545c1334cb

Canonical record JSON

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    "abstract_canon_sha256": "ec277a611c9185f24f482f1c36d00d1bc9bb3b6a83aff4acb6936f4d314887f9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-12T21:44:02Z",
    "title_canon_sha256": "94bbd7c39d0359c3f42b2efe7afac362ef27ad29fcb8ce0283b20722df859ef9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12777",
    "kind": "arxiv",
    "version": 1
  }
}