{"paper":{"title":"Mesoscopic linear statistics of Wigner matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Lodhia, N. J. Simm","submitted_at":"2015-03-11T23:18:52Z","abstract_excerpt":"We study linear spectral statistics of $N \\times N$ Wigner random matrices $\\mathcal{H}$ on mesoscopic scales. Under mild assumptions on the matrix entries of $\\mathcal{H}$, we prove that after centering and normalizing, the trace of the resolvent $\\mathrm{Tr}(\\mathcal{H}-z)^{-1}$ converges to a stationary Gaussian process as $N \\to \\infty$ on scales $N^{-1/3} \\ll \\mathrm{Im}(z) \\ll 1$ and explicitly compute the covariance structure. The limit process is related to certain regularizations of fractional Brownian motion and logarithmically correlated fields appearing in \\cite{FKS13}. Finally, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03533","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"}