{"paper":{"title":"Invariance principles for pruning processes of Galton-Watson trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hui He, Matthias Winkel","submitted_at":"2014-09-03T10:00:15Z","abstract_excerpt":"Pruning processes $(\\mathcal{F}(\\theta),\\theta\\geq 0)$ have been studied separately for Galton-Watson trees and for L\\'evy trees/forests. We establish here a limit theory that strongly connects the two studies. This solves an open problem by Abraham and Delmas, also formulated as a conjecture by L\\\"ohr, Voisin and Winter. Specifically, we show that for any sequence of Galton-Watson forests $\\mathcal{F}_n$, $n\\geq 1$, in the domain of attraction of a L\\'evy forest $\\mathcal{F}$, suitably scaled pruning processes $(\\mathcal{F}_n(\\theta),\\theta\\geq 0)$ converge in the Skorohod topology on cadlag "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1014","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"}