{"paper":{"title":"On percolation in Poisson graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cecilia Holmgren, Johan Bj\\\"orklund, Victor Falgas-Ravry","submitted_at":"2014-11-25T00:06:53Z","abstract_excerpt":"Equip each point $x$ of a homogeneous Poisson process $\\mathcal{P}$ on $\\mathbb{R}$ with $D_x$ edge stubs, where the $D_x$ are i.i.d. positive integer-valued random variables with distribution given by $\\mu$. Following the stable multi-matching scheme introduced by Deijfen, H\\\"aggstrom and Holroyd (2012), we pair off edge stubs in a series of rounds to form the edge set of an infinite component $G$ on the vertex set $\\mathcal{P}$. In this note, we answer questions of Deijfen, Holroyd and Peres (2011) and Deijfen, H\\\"aggstr\\\"om and Holroyd (2012) on percolation (the existence of an infinite con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6688","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"}