{"paper":{"title":"Limit theorems for extrema of Airy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Riddhipratim Basu, Sudeshna Bhattacharjee","submitted_at":"2024-06-17T17:58:44Z","abstract_excerpt":"We establish limit theorems for the maxima and minima of Airy$_1$ and Airy$_2$ processes (denoted by $\\mathcal{A}_1(\\cdot)$ and $\\mathcal{A}_2(\\cdot)$ respectively) over growing intervals. In particular, we identify the finite non-zero constants that are the almost sure limits of $(\\log t)^{-2/3}\\max_{0\\le s \\le t} \\mathcal{A}_{i}(s)$ and $(\\log t)^{-1/3}\\min_{0\\le s \\le t} \\mathcal{A}_{i}(s)$ for $i=1,2$. This complements and extends the results of (Pu, 2023), where the question for the maxima was considered and the order of growth was identified for both $\\mathcal{A}_1$ and $\\mathcal{A}_2$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.11826","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/2406.11826/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"}