{"paper":{"title":"Asymptotics for a class of planar orthogonal polynomials and truncated unitary matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Alfredo Dea\\~no, Kenneth T-R McLaughlin, Leslie Molag, Nick Simm","submitted_at":"2025-05-19T02:39:17Z","abstract_excerpt":"We carry out the asymptotic analysis as $n \\to \\infty$ of a class of orthogonal polynomials $p_{n}(z)$ of degree $n$, defined with respect to the planar measure \\begin{equation*} d\\mu(z) = (1-|z|^{2})^{\\alpha-1}|z-x|^{\\gamma}\\mathbf{1}_{|z| < 1}d^{2}z, \\end{equation*} where $d^{2}z$ is the two dimensional area measure, $\\alpha$ is a parameter that can grow with $n$, while $\\gamma>-2$ and $x>0$ are fixed. This measure arises naturally in the study of characteristic polynomials of non-Hermitian ensembles and generalises the example of a Gaussian weight that was recently studied by several author"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12633","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.12633/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"}