{"paper":{"title":"Birth and death processes on certain random trees: Classification and stationary laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guy Fayolle (INRIA Rocquencourt), Jean-Marc Lasgouttes (INRIA Rocquencourt), Maxim Krikun (LLRS)","submitted_at":"2012-07-16T13:06:10Z","abstract_excerpt":"The main substance of the paper concerns the growth rate and the classification (ergodicity, transience) of a family of random trees. In the basic model, new edges appear according to a Poisson process of parameter $\\lambda$ and leaves can be deleted at a rate $\\mu$. The main results lay the stress on the famous number $e$. A complete classification of the process is given in terms of the intensity factor $\\rho=\\lambda/\\mu $: it is ergodic if $\\rho\\leq e^{-1}$, and transient if $\\rho>e^{-1}$. There is a phase transition phenomenon: the usual region of null recurrence (in the parameter space) h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3664","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"}