{"paper":{"title":"Local Large deviation: A McMillian Theorem for Coloured Random Graph Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Kwabena Doku-Amponsah","submitted_at":"2017-07-06T22:00:27Z","abstract_excerpt":"For a finite typed graph on $n$ nodes and with type law $\\mu,$ we define the so-called spectral potential $\\rho_{\\lambda}(\\,\\cdot,\\,\\mu),$ of the graph.From the $\\rho_{\\lambda}(\\,\\cdot,\\,\\mu)$ we obtain Kullback action or the deviation function, $\\mathcal{H}_{\\lambda}(\\pi\\,\\|\\,\\nu),$ with respect to an empirical pair measure, $\\pi,$ as the Legendre dual.\n  For the finite typed random graph conditioned to have an empirical link measure $\\pi$ and empirical type measure $\\mu$, we prove a Local large deviation principle (LLDP), with rate function $\\mathcal{H}_{\\lambda}(\\pi\\,\\|\\,\\nu)$ and speed $n."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01978","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"}