{"paper":{"title":"Stein-Malliavin Approximations for Nonlinear Functionals of Random Eigenfunctions on ${\\mathbb{S}}^{d}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Domenico Marinucci, Maurizia Rossi","submitted_at":"2014-05-14T10:56:00Z","abstract_excerpt":"We investigate Stein-Malliavin approximations for nonlinear functionals of geometric interest of Gaussian random eigenfunctions on the unit $d$ -dimensional sphere ${\\mathbb{S}}^{d},$ $d\\geq 2.$ All our results are established in the high energy limit, i.e. for eigenfunctions corresponding to growing eigenvalues. More precisely, we provide an asymptotic analysis for the variance of random eigenfunctions, and also establish rates of convergence for various probability metrics for Hermite subordinated processes, arbitrary polynomials of finite order and square integral nonlinear transforms; the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3449","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":""},"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"}