{"paper":{"title":"Scheduling of non-colliding random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Allan Sly, Riddhipratim Basu, Vladas Sidoravicius","submitted_at":"2014-11-14T20:59:23Z","abstract_excerpt":"On the complete graph ${\\cal{K}}_M$ with $M \\ge3$ vertices consider two independent discrete time random walks $\\mathbb{X}$ and $\\mathbb{Y}$, choosing their steps uniformly at random. A pair of trajectories $\\mathbb{X} = \\{ X_1, X_2, \\dots \\}$ and $\\mathbb{Y} = \\{Y_1, Y_2, \\dots \\}$ is called {\\it{non-colliding}}, if by delaying their jump times one can keep both walks at distinct vertices forever. It was conjectured by P. Winkler that for large enough $M$ the set of pairs of non-colliding trajectories $\\{\\mathbb{X},\\mathbb{Y} \\} $ has positive measure. N. Alon translated this problem to the l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4041","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"}