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Axelsson-Fisk and H\\\"aggstr\\\"om established for this model a phase transition for the asymptotic linear speed $\\overline{\\mathrm{v}}$ of the walk. Namely, there exists some critical value $\\lambda_{\\mathrm{c}}>0$ such that $\\overline{\\mathrm{v}}>0$ if $\\lambda\\in (0,\\lambda_{\\mathrm{c}})$ and $\\overline{\\mathrm{v}}=0$ if $\\lambda>\\lambda_{\\mathrm{c}}$.\n  We show that the speed $\\overline{\\mathrm{v}}$ is continuous in $\\lambda$ on the interval $(0,\\lambda_{\\mathrm{c}})$ "},"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":"1705.00671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-01T19:17:08Z","cross_cats_sorted":[],"title_canon_sha256":"3502b653c003cec8db13af6ebe5d7c959f857e2abacbba52a4f89913893ea5d6","abstract_canon_sha256":"beb4d68d607ba3b13685ef25a91e2d9358b88925d702f14b7200ce09081799dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:30.618413Z","signature_b64":"Dh0VCKAxcoZ3BgwUCODMFnC0lRT2RAiOKqdyNkMBzIaRRpIE0uo5zE4P/XaYAXCTX8xpumTokqpCqBtjHv6zBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06af9596efdc5b4072163401be65b270b0bfba1a7a13dc8345d68ce098c549ee","last_reissued_at":"2026-05-18T00:19:30.617924Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:30.617924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity of the speed of 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":"Matthias Meiners, Nina Gantert, Sebastian Mueller","submitted_at":"2017-05-01T19:17:08Z","abstract_excerpt":"We consider biased random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. 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