{"paper":{"title":"Joint large deviation result for empirical measures of the coloured random geometric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kwabena Doku-Amponsah","submitted_at":"2014-06-12T09:47:37Z","abstract_excerpt":"We prove joint large deviation principle for the \\emph{ empirical pair measure} and \\emph{empirical locality measure} of the \\emph{near intermediate} coloured random geometric graph models on $n$ points picked uniformly in a $d-$dimensional torus of a unit circumference.From this result we obtain large deviation principles for the \\emph{number of edges per vertex}, the \\emph{degree distribution and the proportion of isolated vertices } for the \\emph{near intermediate} random geometric graph models."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3171","kind":"arxiv","version":4},"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"}