{"paper":{"title":"Small gaps of GSE","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dong Yao, Jiaming Li, Renjie Feng","submitted_at":"2024-09-05T07:53:06Z","abstract_excerpt":"In this paper, we study the smallest gaps for the Gaussian symplectic ensemble (GSE). We prove that the rescaled smallest gaps and their locations converge to a Poisson point process with an explicit rate. The approach provides an alternative proof for the GOE case and complements the results in \\cite{FTW}. By combining the main results from \\cite{BB, FTW, FW2}, the study of the smallest gaps for the classical random matrix ensembles C$\\beta$E and G$\\beta$E for $\\beta = 1, 2,$ and $4$ is now complete."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.03324","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/2409.03324/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"}