{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/matrix-models-for-beta-ensembles","title":"Matrix Models for Beta Ensembles","arxiv_id":"math-ph/0206043","date":"2002-06-25","proceeding":null,"authors":["Ioana Dumitriu","Alan Edelman"],"abstract":"This paper constructs tridiagonal random matrix models for general ($\\beta>0$) $\\beta$-Hermite (Gaussian) and $\\beta$-Laguerre (Wishart) ensembles. These generalize the well-known Gaussian and Wishart models for $\\beta = 1,2,4$. Furthermore, in the cases of the $\\beta$-Laguerre ensembles, we eliminate the exponent quantization present in the previously known models. We further discuss applications for the new matrix models, and present some open problems.","url_abs":"https://arxiv.org/abs/math-ph/0206043v1","url_pdf":"https://arxiv.org/pdf/math-ph/0206043v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"matrix-models-for-beta-ensembles","repo_url":"https://github.com/AlejandroSantorum/scikit-rmt","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"matrix-models-for-beta-ensembles","repo_url":"https://github.com/JuliaMath/RandomMatrices.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"matrix-models-for-beta-ensembles","repo_url":"https://github.com/UnofficialJuliaMirror/RandomMatrices.jl-2576dda1-a324-5b11-aa66-c48ed7e3c618","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"matrix-models-for-beta-ensembles","repo_url":"https://github.com/UnofficialJuliaMirrorSnapshots/RandomMatrices.jl-2576dda1-a324-5b11-aa66-c48ed7e3c618","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}