{"paper":{"title":"On the speed of biased random walk in translation invariant percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Maria Deijfen, Olle H\\\"aggstr\\\"om","submitted_at":"2010-12-15T16:57:07Z","abstract_excerpt":"For biased random walk on the infinite cluster in supercritical i.i.d.\\ percolation on $\\Z^2$, where the bias of the walk is quantified by a parameter $\\beta>1$, it has been conjectured (and partly proved) that there exists a critical value $\\beta_c>1$ such that the walk has positive speed when $\\beta<\\beta_c$ and speed zero when $\\beta>\\beta_c$. In this paper, biased random walk on the infinite cluster of a certain translation invariant percolation process on $\\Z^2$ is considered. The example is shown to exhibit the opposite behavior to what is expected for i.i.d.\\ percolation, in the sense t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3386","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"}