{"paper":{"title":"Cylinders' percolation in three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Augusto Teixeira, Marcelo Hil\\'ario, Vladas Sidoravicius","submitted_at":"2012-02-08T13:01:04Z","abstract_excerpt":"We study the complementary set of a Poissonian ensemble of infinite cylinders in R^3, for which an intensity parameter u > 0 controls the amount of cylinders to be removed from the ambient space. We establish a non-trivial phase transition, for the existence of an unbounded connected component of this set, as u crosses a critical non-degenerate intensity u*. We moreover show that this complementary set percolates in a sufficiently thick slab, in spite of the fact that it does not percolate in any given plane of R^3, regardless of the choice of u."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1684","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"}