{"paper":{"title":"Einstein relation for 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":"Matthias Meiners, Nina Gantert, Sebastian M\\\"uller","submitted_at":"2018-12-27T17:25:42Z","abstract_excerpt":"We consider random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. In a companion paper, we have shown that if the random walk is pulled to the right by a positive bias $\\lambda > 0$, then its asymptotic linear speed $\\overline{\\mathrm{v}}$ is continuous in the variable $\\lambda > 0$ and differentiable for all sufficiently small $\\lambda > 0$. In the paper at hand, we complement this result by proving that $\\overline{\\mathrm{v}}$ is differentiable at $\\lambda = 0$. Further, we show the Einstein relation for the model, i.e., that the derivativ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10776","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"}