{"paper":{"title":"Difference system for Selberg correlation integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Masahiko Ito, Peter J. Forrester","submitted_at":"2010-11-07T16:39:46Z","abstract_excerpt":"The Selberg correlation integrals are averages of the products $\\prod_{s=1}^m\\prod_{l=1}^n (x_s - z_l)^{\\mu_s}$ with respect to the Selberg density. Our interest is in the case $m=1$, $\\mu_1 = \\mu$, when this corresponds to the $\\mu$-th moment of the corresponding characteristic polynomial. We give the explicit form of a $(n+1) \\times (n+1)$ matrix linear difference system in the variable $\\mu$ which determines the average, and we give the Gauss decomposition of the corresponding $(n+1) \\times (n+1)$ matrix. For $\\mu$ a positive integer the difference system can be used to efficiently compute "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1650","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":""},"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"}