{"paper":{"title":"Anticoncentration of the Permanent in Ginibre Ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math-ph","math.MP","quant-ph"],"primary_cat":"math.PR","authors_text":"Frederic Koehler, Pui Kuen Leung","submitted_at":"2026-07-22T16:15:28Z","abstract_excerpt":"Let $\\mathbb{K}\\in\\{\\mathbb{R},\\mathbb{C},\\mathbb{H}\\}$, put $\\beta=\\dim_{\\mathbb{R}}\\mathbb{K}$, and let $G_n^{\\mathbb{K}}$ be an $n\\times n$ matrix with i.i.d. standard $\\mathbb{K}$-Gaussian entries, namely a standard $\\mathbb{K}$-Ginibre matrix. We prove that the normalized row-ordered permanent $W_n^{\\mathbb{K}}=\\operatorname{per}_{\\mathbb{K}}G_n^{\\mathbb{K}}/\\sqrt{n!}$ has a radial density $p_n^{\\mathbb{K}}$ satisfying $\\|p_n^{\\mathbb{K}}\\|_\\infty=p_n^{\\mathbb{K}}(0)\\lesssim_\\beta n^{(\\beta+2)/4}$ and $\\sup_{z\\in\\mathbb{K}}\\mathbb{P}(|W_n^{\\mathbb{K}}-z|\\leq\\varepsilon)\\lesssim_\\beta n^{("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20329","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/2607.20329/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"}