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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1808.03171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-09T13:59:36Z","cross_cats_sorted":[],"title_canon_sha256":"439801480a74d730dd90d180db123a941faf2d91ecbf964d9b83f66f385f30fb","abstract_canon_sha256":"39d978e8d217ac96731be608d58067713125b6d42f0f95309d6a19aef9f9e304"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:29.982978Z","signature_b64":"IGJ489L2GEbzFJ/pCbwHjSP7s/7HG7Uj6qzPdGSqyX0gy5GuhXr4pPllSpgkqz1QAEKrii0Wh/a14g0BKb/mBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efba7d4eb58fcd582ca2fc8eae3830278e02686e22c85624cb327dda1a36d310","last_reissued_at":"2026-05-18T00:08:29.982584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:29.982584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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