{"paper":{"title":"Orthogonal polynomials for a class of measures with discrete rotational symmetries in the complex plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Dario Merzi, Ferenc Balogh, Tamara Grava","submitted_at":"2015-09-17T16:59:13Z","abstract_excerpt":"We obtain the strong asymptotics of polynomials $p_n(\\lambda)$, $\\lambda\\in\\mathbb{C}$, orthogonal with respect to measures in the complex plane of the form $$ e^{-N(|\\lambda|^{2s}-t\\lambda^s-\\overline{t\\lambda}^s)}dA(\\lambda), $$ where $s$ is a positive integer, $t$ is a complex parameter and $dA$ stands for the area measure in the plane. Such problem has its origin from normal matrix models. We study the asymptotic behaviour of $p_n(\\lambda)$ in the limit $n,N\\to\\infty$ in such a way that $n/N\\to T$ constant. Such asymptotic behaviour has two distinguished regimes according to the topology o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05331","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"}