{"paper":{"title":"Muttalib--Borodin ensembles in random matrix theory --- realisations and correlation functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Dong Wang, Peter J. Forrester","submitted_at":"2015-02-25T12:19:39Z","abstract_excerpt":"Muttalib--Borodin ensembles are characterised by the pair interaction term in the eigenvalue probability density function being of the form $\\prod_{1 \\le j < k \\le N}(\\lambda_k - \\lambda_j) (\\lambda_k^\\theta - \\lambda_j^\\theta)$. We study the Laguerre and Jacobi versions of this model --- so named by the form of the one-body interaction terms --- and show that for $\\theta \\in \\mathbb Z^+$ they can be realised as the eigenvalue PDF of certain random matrices with Gaussian entries. For general $\\theta > 0$, realisations in terms of the eigenvalue PDF of ensembles involving triangular matrices ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07147","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","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"}