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This problem originates from the information theory of single-user multiple-input multiple-output (MIMO) systems studied by Chen and McKay [{\\em IEEE Trans. Inf. Theory} {\\bf 58} ({2012}) {4594--4634}]. By using the ladder operators for orthogonal polynomials with general Laguerre-type weights, we obtain a system of difference equations a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":true},"canonical_record":{"source":{"id":"2510.06739","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-10-08T07:52:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ad5b1f1d673f17793012128bc1a911df026ddf98f54c741c5d050131491f6402","abstract_canon_sha256":"505bab55cdc2a53e87ced7e11163fde8d0ef0fb3d0fcd1a267bcc6a985462cd0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:16.878673Z","signature_b64":"GHoiD/46fS7F2wOdlnXR7UYstQfYwl9zphxy7Uz/2y1W1Uo6V0h5v5nkHzJFTfgSVgfIAONfd3lCqASfCK0eDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b7a1f113a106b06947eff690f0ac8fb52e4a27aa3ec9330e971dad57d4a3a1b","last_reissued_at":"2026-06-05T01:15:16.877896Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:16.877896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics of the Hankel determinant and orthogonal polynomials arising from the information theory of MIMO systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"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.","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Chao Min, Xiaoqing Wu","submitted_at":"2025-10-08T07:52:33Z","abstract_excerpt":"We consider the Hankel determinant and orthogonal polynomials with respect to the deformed Laguerre weight $w(x; t) = {x^\\alpha }{\\mathrm e^{ - x}}{(x + t)^\\lambda },\\; x\\in \\mathbb{R}^{+} $ with parameters $\\alpha > -1,\\; t > 0$ and $\\lambda \\in \\mathbb{R}$. This problem originates from the information theory of single-user multiple-input multiple-output (MIMO) systems studied by Chen and McKay [{\\em IEEE Trans. Inf. Theory} {\\bf 58} ({2012}) {4594--4634}]. By using the ladder operators for orthogonal polynomials with general Laguerre-type weights, we obtain a system of difference equations a"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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+.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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 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