{"paper":{"title":"Asymptotic expansion of the partition function for $\\beta$-ensembles with complex potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alex Little, Alice Guionnet, Karol Kozlowski","submitted_at":"2024-11-15T22:21:38Z","abstract_excerpt":"In this work we establish under certain hypotheses the $N \\to +\\infty$ asymptotic expansion of integrals of the form $$\\mathcal{Z}_{N,\\Gamma}[V] \\, = \\, \\int_{\\Gamma^N} \\prod_{ a < b}^{N}(z_a - z_b)^\\beta \\, \\prod_{k=1}^{N} \\mathrm{e}^{ - N \\beta V(z_k) } \\, \\mathrm{d}\\mathbf{z}$$ where $V \\in \\mathbb{C}[X]$, $\\beta \\in 2 \\mathbb{N}^*$ is an even integer and $\\Gamma \\subset \\mathbb{C}$ is an unbounded contour such that the integral converges. For even degree, real valued $V$s and when $\\Gamma = \\mathbb{R}$, it is well known that the large-$N$ expansion is characterised by an equilibrium measur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.10610","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/2411.10610/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"}