{"paper":{"title":"Rumor processes in random environment on N and on Galton-Watson trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniela Bertacchi, Fabio Zucca","submitted_at":"2013-05-29T13:53:07Z","abstract_excerpt":"The aim of this paper is to study rumor processes in random environment. In a rumor process a signal starts from the stations of a fixed vertex (the root) and travels on a graph from vertex to vertex. We consider two rumor processes. In the firework process each station, when reached by the signal, transmits it up to a random distance. In the reverse firework process, on the other hand, stations do not send any signal but they \"listen\" for it up to a random distance. The first random environment that we consider is the deterministic 1-dimensional tree N with a random number of stations on each"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6802","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":""},"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"}