{"paper":{"title":"Extended Convergence of the Extremal Process of Branching Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anton Bovier, Lisa Hartung","submitted_at":"2014-12-18T18:03:13Z","abstract_excerpt":"We extend the results of Arguin et al and A\\\"\\i{}d\\'ekon et al on the convergence of the extremal process of branching Brownian motion by adding an extra dimension that encodes the \"location\" of the particle in the underlying Galton-Watson tree. We show that the limit is a cluster point process on $\\mathbb{R}_+\\times \\mathbb{R}$ where each cluster is the atom of a Poisson point process on $\\mathbb{R}_+\\times \\mathbb{R}$ with a random intensity measure $Z(dz) \\times Ce^{-\\sqrt 2x}dx$, where the random measure is explicitly constructed from the derivative martingale. This work is motivated by an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5975","kind":"arxiv","version":3},"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"}