{"paper":{"title":"Branching Random Walks on relatively hyperbolic groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.PR","authors_text":"Longmin Wang, Matthieu Dussaule, Wenyuan Yang","submitted_at":"2022-11-14T09:03:34Z","abstract_excerpt":"Let $\\Gamma$ be a non-elementary relatively hyperbolic group with a finite generating set. Consider a finitely supported admissible and symmetric probability measure $\\mu$ on $\\Gamma$ and a probability measure $\\nu$ on $\\mathbb{N}$ with mean $r$. Let $\\mathrm{BRW}(\\Gamma,\\nu,\\mu)$ be the branching random walk on $\\Gamma$ with offspring distribution $\\nu$ and base motion given by the random walk with step distribution $\\mu$. It is known that for $1 < r \\leq R$ with $R$ the radius of convergence for the Green function of the random walk, the population of $\\mathrm{BRW}(\\Gamma,\\nu,\\mu)$ survives "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.07213","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.07213/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}