{"paper":{"title":"Connecting the Random Connection Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Srikanth K. Iyer","submitted_at":"2015-10-19T12:07:11Z","abstract_excerpt":"Consider the random graph $G({\\mathcal P}_{n},r)$ whose vertex set ${\\mathcal P}_{n}$ is a Poisson point process of intensity $n$ on $(- \\frac{1}{2}, \\frac{1}{2}]^d$, $d \\geq 2$. Any two vertices $X_i,X_j \\in {\\mathcal P}_{n}$ are connected by an edge with probability $g\\left( \\frac{d(X_i,X_j)}{r} \\right)$, independently of all other edges, and independent of the other points of ${\\mathcal P}_{n}$. $d$ is the toroidal metric, $r > 0$ and $g:[0,\\infty) \\to [0,1]$ is non-increasing and $\\alpha = \\int_{\\mathbb{R}^d} g(|x|) dx < \\infty$. Under suitable conditions on $g$, almost surely, the critica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05440","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"}