{"paper":{"title":"On the distribution of free-path lengths for the periodic Lorentz gas III","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Emanuele Caglioti, Francois Golse","submitted_at":"2003-01-25T19:28:06Z","abstract_excerpt":"In a flat 2-torus with a disk of diameter $r$ removed, let $\\Phi_r(t)$ be the distribution of free-path lengths (the probability that a segment of length larger than $t$ with uniformly distributed origin and direction does not meet the disk).\n  We prove that $\\Phi_r(t/r)$ behaves like $\\frac{2}{\\pi^2 t}$ for each $t>2$ and in the limit as $r\\to 0^+$, in some appropriate sense.\n  We then discuss the implications of this result in the context of kinetic theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301300","kind":"arxiv","version":1},"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"}