{"paper":{"title":"Uniform regular weighted graphs with large degree: Wigner's law, asymptotic freeness and graphons limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OA"],"primary_cat":"math.PR","authors_text":"Camille Male, Sandrine P\\'ech\\'e","submitted_at":"2014-10-29T19:58:58Z","abstract_excerpt":"For each $N\\geq 1$, let $G_N$ be a simple random graph on the set of vertices $[N]=\\{1,2, ..., N\\}$, which is invariant by relabeling of the vertices. The asymptotic behavior as $N$ goes to infinity of correlation functions:\n  $$ \\mathfrak C_N(T)= \\mathbb E\\bigg[ \\prod_{(i,j) \\in T} \\Big(\\mathbf 1_{\\big(\\{i,j\\} \\in G_N \\big)} - \\mathbb P(\\{i,j\\} \\in G_N) \\Big)\\bigg], \\ T \\subset [N]^2 \\textrm{finite}$$ furnishes informations on the asymptotic spectral properties of the adjacency matrix $A_N$ of $G_N$. Denote by $d_N = N\\times \\mathbb P(\\{i,j\\} \\in G_N) $ and assume $d_N, N-d_N\\underset{N \\righ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8126","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"}