{"paper":{"title":"A robust Khintchine inequality, and algorithms for computing optimal constants in Fourier analysis and high-dimensional geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"cs.CC","authors_text":"Anindya De, Ilias Diakonikolas, Rocco A. Servedio","submitted_at":"2012-07-10T06:27:44Z","abstract_excerpt":"This paper makes two contributions towards determining some well-studied optimal constants in Fourier analysis \\newa{of Boolean functions} and high-dimensional geometry.\n  \\begin{enumerate}\n  \\item It has been known since 1994 \\cite{GL:94} that every linear threshold function has squared Fourier mass at least 1/2 on its degree-0 and degree-1 coefficients. Denote the minimum such Fourier mass by $\\w^{\\leq 1}[\\ltf]$, where the minimum is taken over all $n$-variable linear threshold functions and all $n \\ge 0$. Benjamini, Kalai and Schramm \\cite{BKS:99} have conjectured that the true value of $\\w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2229","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"}