{"paper":{"title":"Determinantal processes and completeness of random exponentials: the critical case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.PR","authors_text":"Subhro Ghosh","submitted_at":"2012-11-11T16:55:44Z","abstract_excerpt":"For a locally finite point set $\\Lambda \\subset \\mathbb{R}$, consider the collection of exponential functions given by $\\mathcal{E}_{\\Lambda}:= \\{e^{i \\lambda x} : \\lambda \\in L \\}$. We examine the question whether $\\mathcal{E}_{\\Lambda}$ spans the Hilbert space $L^2[-\\pi,\\pi]$, when $\\Lambda$ is random. For several point processes of interest, this belongs to a certain critical case of the corresponding question for deterministic $\\Lambda$, about which little is known. For $\\Lambda$ the continuum sine kernel process, obtained as the bulk limit of GUE eigenvalues, we establish that $\\mathcal{E"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2435","kind":"arxiv","version":3},"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"}