{"paper":{"title":"Fine structure in the large n limit of the non-hermitian Penner matrix model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Elena Medina, Gabriel \\'Alvarez, Luis Mart\\'inez Alonso","submitted_at":"2015-07-09T06:16:12Z","abstract_excerpt":"In this paper we apply results on the asymptotic zero distribution of the Laguerre polynomials to discuss generalizations of the standard large $n$ limit in the non-hermitian Penner matrix model. In these generalizations $g_n n\\to t$, but the product $g_n n$ is not necessarily fixed to the value of the 't Hooft coupling $t$. If $t>1$ and the limit $l = \\lim_{n\\rightarrow \\infty} |\\sin(\\pi/g_n)|^{1/n}$ exists, then the large $n$ limit is well-defined but depends both on $t$ and on $l$. This result implies that for $t>1$ the standard large $n$ limit with $g_n n=t$ fixed is not well-defined. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02386","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"}