{"paper":{"title":"Generating stationary random graphs on $\\mathbb{Z}$ with prescribed i.i.d.\\ degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Maria Deijfen, Ronald Meester","submitted_at":"2015-09-23T14:02:49Z","abstract_excerpt":"Let $F$ be a probability distribution with support on the non-negative integers. Two algorithms are described for generating a stationary random graph, with vertex set $\\mathbb{Z}$, so that the degrees of the vertices are i.i.d.\\ random variables with distribution $F$. Focus is on an algorithm where, initially, a random number of \"stubs\" with distribution $F$ is attached to each vertex. Each stub is then randomly assigned a direction, left or right, and the edge configuration is obtained by pairing stubs pointing to each other, first exhausting all possible connections between nearest neighbor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06989","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"}