{"paper":{"title":"Fluctuations of Linear Eigenvalue Statistics of Random Band Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Soshnikov, Indrajit Jana, Koushik Saha","submitted_at":"2014-12-08T04:50:35Z","abstract_excerpt":"In this paper, we study the fluctuation of linear eigenvalue statistics of Random Band Matrices defined by $M_{n}=\\frac{1}{\\sqrt{b_{n}}}W_{n}$, where $W_{n}$ is a $n\\times n$ band Hermitian random matrix of bandwidth $b_{n}$, i.e., the diagonal elements and only first $b_{n}$ off diagonal elements are nonzero. Also variances of the matrix elmements are upto a order of constant. We study the linear eigenvalue statistics $\\mathcal{N}(\\phi)=\\sum_{i=1}^{n}\\phi(\\lambda_{i})$ of such matrices, where $\\lambda_{i}$ are the eigenvalues of $M_{n}$ and $\\phi$ is a sufficiently smooth function. We prove t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2445","kind":"arxiv","version":2},"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"}