{"paper":{"title":"Interlacing adjacent levels of $\\beta$--Jacobi corners processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.QA","math.RT"],"primary_cat":"math.PR","authors_text":"Lingfu Zhang, Vadim Gorin","submitted_at":"2016-12-07T16:42:15Z","abstract_excerpt":"We study the asymptotics of the global fluctuations for the difference between two adjacent levels in the $\\beta$--Jacobi corners process (multilevel and general $\\beta$ extension of the classical Jacobi ensemble of random matrices). The limit is identified with the derivative of the $2d$ Gaussian Free Field. Our main tools are integral forms for the (Macdonald-type) difference operators originating from the shuffle algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02321","kind":"arxiv","version":2},"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"}