{"paper":{"title":"Frogs on trees?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jonathan Hermon","submitted_at":"2016-09-28T02:30:50Z","abstract_excerpt":"We study a system of simple random walks on $\\mathcal{T}_{d,n} = \\mathcal{V}_{d,n}, \\mathcal{E}_{d,n})$, the $d$-ary tree of depth $n$, known as the frog model. Initially there are Pois($\\lambda$) particles at each site, independently, with one additional particle planted at some vertex $\\mathbf{o}$. Initially all particles are inactive, except for the ones which are placed at $\\mathbf{o}$. Active particles perform (independent) $ t \\in \\mathbb{N} \\cup \\{\\infty \\} $ steps of simple random walk on the tree. When an active particle hits an inactive particle, the latter becomes active. The model "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08738","kind":"arxiv","version":5},"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"}