{"paper":{"title":"Central limit theorem for eigenvectors of heavy tailed matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alice Guionnet, Florent Benaych-Georges (MAP5)","submitted_at":"2013-10-28T14:48:47Z","abstract_excerpt":"We consider the eigenvectors of symmetric matrices with independent heavy tailed entries, such as matrices with entries in the domain of attraction of $\\alpha$-stable laws, or adjacencymatrices of Erdos-Renyi graphs. We denote by $U=[u_{ij}]$ the eigenvectors matrix (corresponding to increasing eigenvalues) and prove that the bivariate process $$B^n_{s,t}:=n^{-1/2}\\sum_{1\\le i\\le ns, 1\\le j\\le nt}(|u_{ij}|^2 -n^{-1}),$$ indexed by $s,t\\in [0,1]$, converges in law to a non trivial Gaussian process. An interesting part of this result is the $n^{-1/2}$ rescaling, proving that from this point of v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7435","kind":"arxiv","version":3},"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"}