{"paper":{"title":"Local convergence of critical random trees and continuous-state branching processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xin He","submitted_at":"2015-03-03T14:14:51Z","abstract_excerpt":"We study the local convergence of critical Galton-Watson trees and Levy trees under various conditionings. Assuming a very general monotonicity property on the functional of random trees, we show that random trees conditioned to have large functional values always converge locally to immortal trees. We also derive a very general ratio limit property for functionals of random trees satisfying the monotonicity property. Then we move on to study the local convergence of critical continuous-state branching processes, and prove a similar result. Finally we give a definition of continuum condensatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00951","kind":"arxiv","version":2},"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"}