{"paper":{"title":"Free energy expansions of a conditional GinUE and large deviations of the smallest eigenvalue of the LUE","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Meng Yang, Seong-Mi Seo, Sung-Soo Byun","submitted_at":"2024-02-29T09:38:37Z","abstract_excerpt":"We consider a planar Coulomb gas ensemble of size $N$ with the inverse temperature $\\beta=2$ and external potential $Q(z)=|z|^2-2c \\log|z-a|$, where $c>0$ and $a \\in \\mathbb{C}$. Equivalently, this model can be realised as $N$ eigenvalues of the complex Ginibre matrix of size $(c+1) N \\times (c+1) N$ conditioned to have deterministic eigenvalue $a$ with multiplicity $cN$. Depending on the values of $c$ and $a$, the droplet reveals a phase transition: it is doubly connected in the post-critical regime and simply connected in the pre-critical regime. In both regimes, we derive precise large-$N$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.18983","kind":"arxiv","version":3},"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/2402.18983/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"}