{"paper":{"title":"Virial estimates for hard spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ryan Denlinger","submitted_at":"2016-05-02T18:29:47Z","abstract_excerpt":"We review a virial-type estimate which bounds the strength of interaction for a gas of $N$ hard spheres (billiard balls) dispersing into Euclidean space $\\mathbb{R}^d$. This type of estimate has been known for decades in the context of (semi-)dispersing billiards, and is essentially trivial in that context. Our goal, however, is to write virial estimates in a way which may lend insight into the problem of rigorously deriving Boltzmann's equation (cf. Lanford's theorem). Using virial estimates, we provide a short proof of lower bounds (sharp up to powers of logarithms) on the convergence rate o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00607","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"}