{"paper":{"title":"Laguerre Expansion for Nodal Volumes and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anna Paola Todino, Domenico Marinucci, Maurizia Rossi","submitted_at":"2023-12-15T17:17:24Z","abstract_excerpt":"We investigate the nodal volume of random hyperspherical harmonics $\\lbrace T_{\\ell;d}\\rbrace_{\\ell\\in \\mathbb N}$ on the $d$-dimensional unit sphere ($d\\ge 2$). We exploit an orthogonal expansion in terms of Laguerre polynomials; this representation entails a drastic reduction in the computational complexity and allows to prove \\emph{isotropy} for chaotic components, an issue which was left open in the previous literature. As a further application, we establish our main result, i.e., variance bounds for the nodal volume in any dimension; for $d\\ge 3$ and as the eigenvalues diverge (i.e., as $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.09962","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/2312.09962/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"}