{"paper":{"title":"Mesoscopic Rates of Convergence for Complex Wishart Matrices at the Leftmost Spectrum Edge","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Laguerre unitary ensemble eigenvalues converge to the Airy process at mesoscopic scales in L1-Wasserstein distance at the left edge","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mengchun Cai","submitted_at":"2026-05-12T21:44:02Z","abstract_excerpt":"This paper establishes mesoscopic rates of convergence in the $L^1$-Wasserstein distance for eigenvalue determinantal point processes (DPPs) derived from the Laguerre Unitary Ensemble (LUE) to the corresponding limiting point process (Airy process) as the dimension goes to infinity. Specifically, we prove convergence rates at the leftmost edge of the LUE spectrum, which corresponds to the least eigenvalue. These results are termed mesoscopic because they allow for a direct comparison of point counts between the convergent DPPs and their limits over a range of scales."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Mesoscopic L1-Wasserstein convergence rates are established for the left-edge eigenvalues of the Laguerre Unitary Ensemble to the Airy point process.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Laguerre unitary ensemble eigenvalues converge to the Airy process at mesoscopic scales in L1-Wasserstein distance at the left edge","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"417067657502f666b2d6da78dd9f6dbca9a27ea560d56caa1fea81243d9a103e"},"source":{"id":"2605.12777","kind":"arxiv","version":1},"verdict":{"id":"37599403-a0a8-4a7f-927c-7cb93d7144dc","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:23:40.495424Z","strongest_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.","one_line_summary":"Mesoscopic L1-Wasserstein convergence rates are established for the left-edge eigenvalues of the Laguerre Unitary Ensemble to the Airy point process.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"Laguerre unitary ensemble eigenvalues converge to the Airy process at mesoscopic scales in L1-Wasserstein distance at the left edge"},"references":{"count":29,"sample":[{"doi":"","year":2015,"title":"Oxford University Press, 1 edition, September 2015","work_id":"33cb11bf-6f5f-4633-98b3-000477899dee","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"Anderson, Alice Guionnet, and Ofer Zeitouni.An introduction to random matrices","work_id":"816be651-2a73-439f-adcf-c4e514253f10","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Szarek.Alice and Bob meet Banach: the interface of asymptotic geometric analysis and quantum information theory","work_id":"4ed9571b-01a7-44d1-a831-f756ccf67702","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1993,"title":"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","work_id":"5b556c7f-5dfa-470d-b44d-620580c3b67a","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"Bai.Spectral analysis of large dimensional random matrices","work_id":"4bc699ad-a4c4-4d0f-9c45-3f64cfd5695e","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":29,"snapshot_sha256":"2cc503b82675a33a5c4cadfe8b42882123279f2bf5348f2663abec753c71d904","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}