{"paper":{"title":"Limit theorems for mixed-norm sequence spaces with applications to volume distribution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Joscha Prochno, Michael Juhos, Zakhar Kabluchko","submitted_at":"2022-09-19T11:43:30Z","abstract_excerpt":"Let $p, q \\in (0, \\infty]$ and $\\ell_p^m(\\ell_q^n)$ be the mixed-norm sequence space of real matrices $x = (x_{i, j})_{i \\leq m, j \\leq n}$ endowed with the (quasi-)norm $\\Vert x \\Vert_{p, q} := \\big\\Vert \\big( \\Vert (x_{i, j})_{j \\leq n} \\Vert_q \\big)_{i \\leq m} \\Vert_p$. We shall prove a Poincar\\'e-Maxwell-Borel lemma for suitably scaled matrices chosen uniformly at random in the $\\ell_p^m(\\ell_q^n)$ unit balls $\\mathbb{B}_{p, q}^{m, n}$, and obtain both central and non-central limit theorems for their $\\ell_p(\\ell_q)$-norms. We use those limit theorems to study the asymptotic volume distrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.08937","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/2209.08937/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"}