{"paper":{"title":"Product Space Models of Correlation: Between Noise Stability and Additive Combinatorics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Elchanan Mossel, Jan H\\k{a}z{\\l}a, Thomas Holenstein","submitted_at":"2015-09-21T11:31:01Z","abstract_excerpt":"There is a common theme to some research questions in additive combinatorics and noise stability. Both study the following basic question: Let $\\mathcal{P}$ be a probability distribution over a space $\\Omega^\\ell$ with all $\\ell$ marginals equal. Let $\\underline{X}^{(1)}, \\ldots, \\underline{X}^{(\\ell)}$ where $\\underline{X}^{(j)} = (X_1^{(j)}, \\ldots, X_n^{(j)})$ be random vectors such that for every coordinate $i \\in [n]$ the tuples $(X_i^{(1)}, \\ldots, X_i^{(\\ell)})$ are i.i.d. according to $\\mathcal{P}$.\n  A central question that is addressed in both areas is:\n  - Does there exist a functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06191","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"}