{"paper":{"title":"Hard-edge asymptotics of the Jacobi growth process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jeffrey Kuan, Mark Cerenzia","submitted_at":"2016-08-23T05:18:16Z","abstract_excerpt":"We introduce a two parameter ($\\alpha, \\beta>-1$) family of interacting particle systems with determinantal correlation kernels expressible in terms of Jacobi polynomials $\\{ P^{(\\alpha, \\beta)}_k \\}_{k \\geq 0}$. The family includes previously discovered Plancherel measures for the infinite-dimensional orthogonal and symplectic groups. The construction uses certain BC-type orthogonal polynomials which generalize the characters of these groups.\n  The local asymptotics near the hard edge where one expects distinguishing behavior yields the multi-time $(\\alpha, \\beta)$-dependent discrete Jacobi k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06384","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"}