{"paper":{"title":"High-dimensional limits and extremizers for maximal functions associated with log-concave densities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.MG","math.PR"],"primary_cat":"math.CA","authors_text":"B{\\l}a\\.zej Wr\\'obel, Valentina Ciccone","submitted_at":"2026-07-07T09:16:36Z","abstract_excerpt":"We introduce a unified framework to establish the high-dimensional asymptotic behavior of maximal functions associated with radial log-concave probability densities, encompassing the maximal heat semigroup, Hardy-Littlewood maximal function over Euclidean balls, and, additionally, maximal spherical means. Namely, for any $p \\in (1, \\infty)$, we prove that the $L^p(\\mathbb{R}^d)$ operator norms of these maximal operators all converge as the dimension $d \\to \\infty$ to a single, universal limit $\\lambda(p)$.\n  Furthermore, by proving that the $L^p$ operator norms for the heat semigroup $\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06041","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/2607.06041/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"}