{"paper":{"title":"Mean of the $L^\\infty$-norm for $L^2$-normalized random waves on compact aperiodic Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP","math.PR","math.SP"],"primary_cat":"math-ph","authors_text":"Boris Hanin, Yaiza Canzani","submitted_at":"2013-10-04T18:32:38Z","abstract_excerpt":"This article concerns upper bounds for $L^\\infty$-norms of random approximate eigenfunctions of the Laplace operator on a compact aperiodic Riemannian manifold $(M,g).$ We study $f_{\\lambda}$ chosen uniformly at random from the space of $L^2$-normalized linear combinations of Laplace eigenfunctions with eigenvalues in the interval $(\\lambda^2, \\lr{\\lambda+1}^2].$ Our main result is that the expected value of $\\norm{f_\\lambda}_\\infty$ grows at most like $C \\sqrt{\\log \\lambda}$ as $\\lambda \\to \\infty$, where $C$ is an explicit constant depending only on the dimension and volume of $(M,g).$ In ad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1361","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":""},"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"}