{"paper":{"title":"Spread of visited sites of a random walk along the generations of a branching process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pierre Andreoletti (MAPMO), Pierre Debs (MAPMO)","submitted_at":"2013-03-13T16:05:28Z","abstract_excerpt":"In this paper we consider a null recurrent random walk in random environment on a super-critical Galton-Watson tree. We consider the case where the log-Laplace transform $\\psi$ of the branching process satisfies $\\psi(1)=\\psi'(1)=0$ for which G. Faraud, Y. Hu and Z. Shi in \\cite{HuShi10b} show that, with probability one, the largest generation visited by the walk, until the instant $n$, is of the order of $(\\log n)^3$. In \\cite{AndreolettiDebs1} we prove that the largest generation entirely visited behaves almost surely like $\\log n$ up to a constant. Here we study how the walk visits the gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3199","kind":"arxiv","version":3},"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"}