{"paper":{"title":"Structure of correlations for the Boltzmann-Grad limit of hard spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ryan Denlinger","submitted_at":"2017-07-07T17:14:01Z","abstract_excerpt":"We consider a gas of $N$ identical hard spheres in the whole space, and we enforce the Boltzmann-Grad scaling. We may suppose that the particles are essentially independent of each other at some initial time; even so, correlations will be created by the dynamics. We will prove a structure theorem for the correlations which develop at positive time. Our result generalizes a previous result which states that there are phase points where the three-particle marginal density factorizes into two-particle and one-particle parts, while further factorization is impossible. The result depends on uniform"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02274","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"}