{"paper":{"title":"The Speed of a Biased Walk on a Galton-Watson Tree without Leaves is Monotonic with Respect to Progeny Distributions for High Values of Bias","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Behzad Mehrdad, Lingjiong Zhu, Sanchayan Sen","submitted_at":"2012-12-12T22:13:36Z","abstract_excerpt":"Consider biased random walks on two Galton-Watson trees without leaves having progeny distributions $P_1$ and $P_2$ (GW$(P_1)$ and GW$(P_2)$) where $P_1$ and $P_2$ are supported on positive integers and $P_1$ dominates $P_2$ stochastically. We prove that the speed of the walk on GW$(P_1)$ is bigger than the same on GW$(P_2)$ when the bias is larger than a threshold depending on $P_1$ and $P_2$. This partially answers a question raised by Ben Arous, Fribergh and Sidoravicius."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3004","kind":"arxiv","version":4},"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"}