{"paper":{"title":"Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"B. Tirozzi, M. Shcherbina","submitted_at":"2009-11-30T16:25:00Z","abstract_excerpt":"We consider the adjacency matrix $A$ of a large random graph and study fluctuations of the function $f_n(z,u)=\\frac{1}{n}\\sum_{k=1}^n\\exp\\{-uG_{kk}(z)\\}$ with $G(z)=(z-iA)^{-1}$. We prove that the moments of fluctuations normalized by $n^{-1/2}$ in the limit $n\\to\\infty$ satisfy the Wick relations for the Gaussian random variables. This allows us to prove central limit theorem for $\\hbox{Tr}G(z)$ and then extend the result on the linear eigenvalue statistics $\\hbox{Tr}\\phi(A)$ of any function $\\phi:\\mathbb{R}\\to\\mathbb{R}$ which increases, together with its first two derivatives, at infinity n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.5684","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"}