{"paper":{"title":"On The Fourier Coefficients of High-Dimensional Random Geometric Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Guy Bresler, Kiril Bangachev","submitted_at":"2024-02-19T22:55:56Z","abstract_excerpt":"The random geometric graph $\\mathsf{RGG}(n,\\mathbb{S}^{d-1}, p)$ is formed by sampling $n$ i.i.d. vectors $\\{V_i\\}_{i = 1}^n$ uniformly on $\\mathbb{S}^{d-1}$ and placing an edge between pairs of vertices $i$ and $j$ for which $\\langle V_i,V_j\\rangle \\ge \\tau^p_d,$ where $\\tau^p_d$ is such that the expected density is $p.$ We study the low-degree Fourier coefficients of the distribution $\\mathsf{RGG}(n,\\mathbb{S}^{d-1}, p)$ and its Gaussian analogue.\n  Our main conceptual contribution is a novel two-step strategy for bounding Fourier coefficients which we believe is more widely applicable to st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.12589","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/2402.12589/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"}