{"paper":{"title":"Decomposition of mean-field Gibbs distributions into product measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Renan Gross, Ronen Eldan","submitted_at":"2017-08-19T15:05:19Z","abstract_excerpt":"We show that under a low complexity condition on the gradient of a Hamiltonian, Gibbs distributions on the Boolean hypercube are approximate mixtures of product measures whose probability vectors are critical points of an associated mean-field functional. This extends a previous work by the first author. As an application, we demonstrate how this framework helps characterize both Ising models satisfying a mean-field condition and the conditional distributions which arise in the emerging theory of nonlinear large deviations, both in the dense case and in the polynomially-sparse case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05859","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"}