Pith Number

pith:DN5B6EJ2

pith:2025:DN5B6EJ2CBVQNFD675UQ6CWI7N

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Asymptotics of the Hankel determinant and orthogonal polynomials arising from the information theory of MIMO systems

Chao Min, Xiaoqing Wu

Dyson's Coulomb fluid approach yields large-n asymptotic expansions for recurrence coefficients, Hankel determinants, and related quantities for orthogonal polynomials with a deformed Laguerre weight from MIMO information theory.

arxiv:2510.06739 v3 · 2025-10-08 · math-ph · math.MP

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Claims

C1strongest claim

By using Dyson's Coulomb fluid approach, we obtain the large n asymptotic expansions of the recurrence coefficients α_n(t) and β_n(t), the sub-leading coefficient p(n, t) of the monic orthogonal polynomials, the Hankel determinant D_n(t) and the normalized constant h_n(t) for fixed t∈R+.

C2weakest assumption

That Dyson's Coulomb fluid approach applies directly to the deformed weight w(x;t) and yields the stated leading asymptotics without further corrections for the (x+t)^λ factor or the specific parameter regime (section on large-n analysis).

C3one line summary

Derives large-n asymptotics for recurrence coefficients α_n(t), β_n(t), Hankel determinant D_n(t), and related quantities for orthogonal polynomials with weight w(x;t)=x^α e^{-x}(x+t)^λ using ladder operators and Dyson's Coulomb fluid approach, plus long-time asymptotics as t→∞.

Formal links

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Receipt and verification

First computed	2026-06-05T01:15:16.877896Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b7a1f113a106b06947eff690f0ac8fb52e4a27aa3ec9330e971dad57d4a3a1b

Aliases

arxiv: 2510.06739 · arxiv_version: 2510.06739v3 · doi: 10.48550/arxiv.2510.06739 · pith_short_12: DN5B6EJ2CBVQ · pith_short_16: DN5B6EJ2CBVQNFD6 · pith_short_8: DN5B6EJ2

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/DN5B6EJ2CBVQNFD675UQ6CWI7N \
  | 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: 1b7a1f113a106b06947eff690f0ac8fb52e4a27aa3ec9330e971dad57d4a3a1b

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "505bab55cdc2a53e87ced7e11163fde8d0ef0fb3d0fcd1a267bcc6a985462cd0",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2025-10-08T07:52:33Z",
    "title_canon_sha256": "ad5b1f1d673f17793012128bc1a911df026ddf98f54c741c5d050131491f6402"
  },
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  "source": {
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    "kind": "arxiv",
    "version": 3
  }
}