{"paper":{"title":"Almost Sure Uniform Convergence Of Random Hermite Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Micka\\\"el Latocca (LaMME), Rafik Imekraz (MIA, ULR)","submitted_at":"2025-06-04T11:43:05Z","abstract_excerpt":"We continue the analysis of random series associated to the multidimensional harmonic oscillator $-\\Delta + |x|^2$ on $\\mathbb{R}^d$ with d \\geq 2$$. More precisely we obtain a necessary and sufficient condition to get the almost sure uniform convergence on the whole space $\\mathbb{R}^d$ . It turns out that the same condition gives the almost sure uniform convergence on the sphere $\\mathbb{S}^{d-1}$ (despite $\\mathbb{S}^{d-1}$ is a zero Lebesgue measure of $\\mathbb{R}^d$). From a probabilistic point of view, our proof adapts a strategy used by the first author for boundaryless Riemannian compa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03858","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/2506.03858/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"}