{"paper":{"title":"The speed of critically biased random walk in a one-dimensional percolation model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jan-Erik L\\\"ubbers, Matthias Meiners","submitted_at":"2018-08-09T13:59:36Z","abstract_excerpt":"We consider biased random walks in a one-dimensional percolation model. This model goes back to Axelson-Fisk and H\\\"aggstr\\\"om and exhibits the same phase transition as biased random walk on the infinite cluster of supercritical Bernoulli bond percolation on $\\mathbb{Z}^d$, namely, for some critical value $\\lambda_{\\mathrm{c}} >0$ of the bias, it holds that the asymptotic linear speed $\\overline{\\mathrm{v}}$ of the walk is strictly positive if the bias $\\lambda$ is strictly smaller than $\\lambda_{\\mathrm{c}}$, whereas $\\overline{\\mathrm{v}}=0$ if $\\lambda \\geq \\lambda_{\\mathrm{c}}$.\n  We show "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03171","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"}