dc.contributor.author | Benaych-Georges, Florent | |
dc.contributor.author | Guionnet, Alice | |
dc.date.accessioned | 2014-09-15T15:31:57Z | |
dc.date.available | 2014-09-15T15:31:57Z | |
dc.date.issued | 2014-06 | |
dc.date.submitted | 2013-10 | |
dc.identifier.issn | 1083-6489 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/89525 | |
dc.description.abstract | We consider the eigenvectors of symmetric matrices with independent heavy tailed entries, such as matrices with entries in the domain of attraction of α-stable laws, or adjacencymatrices of Erdos-Renyi graphs. We denote by U=[uij] the eigenvectors matrix (corresponding to increasing eigenvalues) and prove that the bivariate process [formula] indexed by s,t∈[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 view, the eigenvectors matrix U behaves more like a permutation matrix (as it was proved by Chapuy that for U a permutation matrix, n−1/2 is the right scaling) than like a Haar-distributed orthogonal or unitary matrix (as it was proved by Rouault and Donati-Martin that for U such a matrix, the right scaling is 1). | en_US |
dc.description.sponsorship | Simons Foundation | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (Grant DMS-1307704) | en_US |
dc.language.iso | en_US | |
dc.publisher | Institute of Mathematical Statistics | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1214/EJP.v19-3093 | en_US |
dc.rights | Creative Commons Attribution | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by/2.5/ | en_US |
dc.source | Institute of Mathematical Statistics | en_US |
dc.title | Central limit theorem for eigenvectors of heavy tailed matrices | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Benaych-Georges, Florent, and Alice Guionnet. “Central Limit Theorem for Eigenvectors of Heavy Tailed Matrices.” Electronic Journal of Probability 19, no. 0 (January 2, 2014). | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.mitauthor | Guionnet, Alice | en_US |
dc.relation.journal | Electronic Journal of Probability | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Benaych-Georges, Florent; Guionnet, Alice | en_US |
dc.identifier.orcid | https://orcid.org/0000-0003-4524-8627 | |
mit.license | PUBLISHER_CC | en_US |
mit.metadata.status | Complete | |