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Let $\\mathcal{T}_p$ be percolation on $\\mathcal{T}$ with parameter $p$, and let $p_c = \\mu^{-1}$ be the critical percolation parameter. We consider a random walk $(X_n)_{n \\ge 1}$ on $\\mathcal{T}_p$ and investigate the behavior of the embedded process $\\varphi_{\\mathcal{T}_p}(X_n)$ as $n\\to \\infty$ and simultaneously"},"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":"1804.04396","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-12T09:40:22Z","cross_cats_sorted":[],"title_canon_sha256":"daca60822454e795dc2e40c995ade830d2b9a7fe37fea873c60f6a07836f8a46","abstract_canon_sha256":"5f269ed278e4ed6285ea7ad76ba12a8f20e017fde4bdd69f544d363992205a43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:21.423152Z","signature_b64":"TWq4m3yp13wrifZiB83NLPRvOmUTX/DO+CPx/8qu39dUX9bWsZJ8qFQQOSCPE0w8hCyx4897xXkm3vwrQAz1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95cc450f941dab531a5d6632737ba125a2fb4195e496ec0b77161fa37e7ec2b9","last_reissued_at":"2026-05-17T23:51:21.422571Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:21.422571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random walk on barely supercritical branching random walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jan Nagel, Remco van der Hofstad, Tim Hulshof","submitted_at":"2018-04-12T09:40:22Z","abstract_excerpt":"Let $\\mathcal{T}$ be a supercritical Galton-Watson tree with a bounded offspring distribution that has mean $\\mu >1$, conditioned to survive. 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