{"paper":{"title":"Free energy and fluctuations in the random normal matrix model with spectral gaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Christophe Charlier, Joakim Cronvall, Yacin Ameur","submitted_at":"2023-12-21T14:50:28Z","abstract_excerpt":"We study large $n$ expansions for the partition function of a Coulomb gas $$Z_n=\\frac 1 {\\pi^n}\\int_{\\mathbb{C}^n}\\prod_{1\\le i<j\\le n}|z_i-z_j|^2\\prod_{i=1}^n e^{-nQ(z_i)}\\, d^2 z_i,$$ where $Q$ is a radially symmetric confining potential on the complex plane $\\mathbb{C}$.\n  The droplet is not assumed to be connected, but may consist of a number of disjoint connected annuli and possibly a central disk. The boundary condition is ``soft edge'', i.e., $Q$ is smooth in a $\\mathbb{C}$-neighbourhood of the droplet.\n  We include the following possibilities: (i) existence of ``outposts'', i.e., compo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.13904","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/2312.13904/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"}