{"paper":{"title":"Planar Coulomb gas on a Jordan arc at any temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CV","authors_text":"Fredrik Viklund, Klara Courteaut, Kurt Johansson","submitted_at":"2025-04-28T15:19:09Z","abstract_excerpt":"We study a planar Coulomb gas confined to a sufficiently smooth Jordan arc $\\gamma$ in the complex plane, at inverse temperature $\\beta > 0$. Let \\[\\bar{Z}_{n}^\\beta(\\gamma) = Z_{n}^\\beta(\\gamma)/\\left(2 \\textrm{cap}(\\gamma)\\right)^{\\beta n^2/2+(1-\\beta/2)n}\\] be the normalized partition function. We compute the free energy as the number of particles tends to infinity, including the constant term: \\[ \\lim_{n\\to \\infty}\\log \\frac{\\bar{Z}_{n}^\\beta(\\gamma)}{\\bar{Z}_{n}^\\beta([-1,1])} = \\frac{1}{24}J^A(\\gamma) + \\frac{1}{8} \\left( \\sqrt{ \\frac{\\beta}{2} } - \\sqrt{ \\frac{2}{\\beta}} \\right)^2 J^{F}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.19887","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.19887/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"}