{"paper":{"title":"Computation of marginal eigenvalue distributions in the Laguerre and Jacobi $\\beta$ ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math.MP","math.PR","physics.data-an","stat.CO"],"primary_cat":"math-ph","authors_text":"Peter J. Forrester, Santosh Kumar","submitted_at":"2024-02-25T11:37:49Z","abstract_excerpt":"We consider the problem of the exact computation of the marginal eigenvalue distributions in the Laguerre and Jacobi $\\beta$ ensembles. In the case $\\beta=1$ this is a question of long standing in the mathematical statistics literature. A recursive procedure to accomplish this task is given for $\\beta$ a positive integer, and the parameter $\\lambda_1$ a non-negative integer. This case is special due to a finite basis of elementary functions, with coefficients which are polynomials. In the Laguerre case with $\\beta = 1$ and $\\lambda_1 + 1/2$ a non-negative integer some evidence is given of thei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.16069","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.16069/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}