{"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. Let $\\varphi_{\\mathcal{T}}$ be a random embedding of $\\mathcal{T}$ into $\\mathbb{Z}^d$ according to a simple random walk step distribution. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04396","kind":"arxiv","version":2},"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"}