{"paper":{"title":"Invariant bipartite random graphs on $\\mathbb{R}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabio Lopes","submitted_at":"2012-02-23T18:40:39Z","abstract_excerpt":"Suppose that red and blue points occur in $\\mathbb{R}^d$ according to two simple point process with finite intensities $\\lambda_{\\mathcal{R}}$ and $\\lambda_{\\mathcal{B}}$, respectively. Furthermore, let $\\nu$ and $\\mu$ be two probability distributions on the strictly positive integers. Assign independently a random number of stubs (half-edges) to each red and blue point with laws $\\nu$ and $\\mu$, respectively. We are interested in translation-invariant schemes to match stubs between points of different colors in order to obtain random bipartite graphs in which each point has a prescribed degre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5262","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"}