{"paper":{"title":"Hole probabilities and balayage of measures for planar Coulomb gases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.CA","authors_text":"Christophe Charlier","submitted_at":"2023-11-26T12:57:25Z","abstract_excerpt":"We study hole probabilities of two-dimensional Coulomb gases with a general potential and arbitrary temperature. The hole region $U$ is assumed to satisfy $\\partial U\\subset S$, where $S$ is the support of the equilibrium measure $\\mu$. Let $n$ be the number of points. As $n \\to \\infty$, we prove that the probability that no points lie in $U$ behaves like $\\exp(-Cn^{2}+o(n^{2}))$. We determine $C$ in terms of $\\mu$ and the balayage measure $\\nu = \\mathrm{Bal}(\\mu|_{U},\\partial U)$. If $U$ is unbounded, then $C$ also involves the Green function of $\\Omega$ with pole at $\\infty$, where $\\Omega$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.15285","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/2311.15285/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"}