{"paper":{"title":"Asymptotic properties of expansive Galton-Watson trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Fran\\c{c}ois Delmas (CERMICS), Romain Abraham (MAPMO)","submitted_at":"2017-12-13T08:18:51Z","abstract_excerpt":"We consider a super-critical Galton-Watson tree whose non-degenerate offspring distribution has finite mean. We consider the random trees $\\tau$n distributed as $\\tau$ conditioned on the n-th generation, Zn, to be of size an $\\in$ N. We identify the possible local limits of $\\tau$n as n goes to infinity according to the growth rate of an. In the low regime, the local limit $\\tau$ 0 is the Kesten tree, in the moderate regime the family of local limits, $\\tau$ $\\theta$ for $\\theta$ $\\in$ (0, +$\\infty$), is distributed as $\\tau$ conditionally on {W = $\\theta$}, where W is the (non-trivial) limit "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04650","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"}