{"paper":{"title":"Asymptotics for a special solution of the thirty fourth Painleve equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"A.B.J. Kuijlaars, A.R. Its, J. Ostensson","submitted_at":"2008-11-24T11:33:16Z","abstract_excerpt":"In a previous paper we studied the double scaling limit of unitary random matrix ensembles of the form Z_{n,N}^{-1} |\\det M|^{2\\alpha} e^{-N \\Tr V(M)} dM with \\alpha > -1/2. The factor |\\det M|^{2\\alpha} induces critical eigenvalue behavior near the origin. Under the assumption that the limiting mean eigenvalue density associated with V is regular, and that the origin is a right endpoint of its support, we computed the limiting eigenvalue correlation kernel in the double scaling limit as n, N \\to \\infty such that n^{2/3}(n/N-1) = O(1) by using the Deift-Zhou steepest descent method for the Rie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.3847","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"}