{"paper":{"title":"Smallest gaps of the two-dimensional Coulomb gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Christophe Charlier","submitted_at":"2025-07-31T12:41:33Z","abstract_excerpt":"We consider the two-dimensional Coulomb gas with a general potential at the determinantal temperature, or equivalently, the eigenvalues of random normal matrices. We prove that the smallest gaps between particles are typically of order $n^{-3/4}$, and that the associated joint point process of gap locations and gap sizes, after rescaling the gaps by $n^{3/4}$, converges to a Poisson point process. As a consequence, we show that the $k$-th smallest rescaled gap has a limiting density proportional to $x^{4k-1}e^{-\\frac{\\mathcal{J}}{4}x^{4}}$, where $\\mathcal{J}=\\pi^{2}\\int \\rho(z)^{3}d^{2}z$ and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.23502","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/2507.23502/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"}