{"paper":{"title":"Proof of the Ergodic Hypothesis for Typical Hard Ball Systems","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Nandor Simanyi","submitted_at":"2002-10-17T23:36:25Z","abstract_excerpt":"We consider the system of $N$ ($\\ge2$) hard balls with masses $m_1,...,m_N$ and radius $r$ in the flat torus $\\Bbb T_L^\\nu=\\Bbb R^\\nu/L\\cdot\\Bbb Z^\\nu$ of size $L$, $\\nu\\ge3$. We prove the ergodicity (actually, the Bernoulli mixing property) of such systems for almost every selection $(m_1,...,m_N; L)$ of the outer geometric parameters. This theorem complements my earlier result that proved the same, almost sure ergodicity for the case $\\nu=2$. The method of that proof was primarily dynamical-geometric, whereas the present approach is inherently algebraic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0210280","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"}