{"paper":{"title":"Soft edge limit of the Laguerre beta-ensemble at the lower edge","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Benedek Valk\\'o, Jiaming Xu, Yun Li","submitted_at":"2026-07-09T14:32:22Z","abstract_excerpt":"We show that the lower edge of the appropriately scaled size $n$ Laguerre beta-ensemble with parameter $a=a_n$ converges to the $\\operatorname{Airy}_{\\beta}$ process as $n\\to \\infty$ when $a_n\\to \\infty$ and $\\tfrac{a_n}{n}\\to 0$. This completes the picture of the possible edge scaling limits of the Laguerre beta-ensemble with a fixed $\\beta>0$. When $a_n\\gg (\\log \\log n)^3$ our proof establishes operator level convergence of the inverse of the scaled Dumitriu-Edelman tridiagonal matrix to the inverse of the stochastic Airy operator. Our methods allow us to prove similar operator level limits "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08536","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/2607.08536/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"}