dc.contributor.author Schlein, Benjamin dc.contributor.author Yau, Horng-Tzer dc.contributor.author Yin, Jun dc.date.accessioned 2016-02-17T21:32:42Z dc.date.issued 2012 dc.identifier.citation Erdos, László, Benjamin Schlein, Horng-Tzer Yau, and Jun Yin. 2012. “The Local Relaxation Flow Approach to Universality of the Local Statistics for Random Matrices.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 48 (1) (February): 1–46. doi:10.1214/10-aihp388. en_US dc.identifier.issn 0246-0203 en_US dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:25426537 dc.description.abstract We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides with the local statistics of the corresponding Gaussian ensemble provided the distribution of the individual matrix element is smooth and the eigenvalues {$x_{j}$}$_{j=1}^{N}$ are close to their classical location {$\gamma$$_{j}$}$_{j=1}^{N}$ determined by the limiting density of eigenvalues. Under the scaling where the typical distance between neighboring eigenvalues is of order 1/$N$, the necessary apriori estimate on the location of eigenvalues requires only to know that $\mathbb{E}$ |$x_{j}$ $-$ $\gamma$$_{j}$|$^{2}$ $\leq$ $N$$^{-1-\epsilon}$ on average. This information can be obtained by well established methods for various matrix ensembles. We demonstrate the method by proving local spectral universality for Wishart matrices. en_US dc.description.sponsorship Mathematics en_US dc.language.iso en_US en_US dc.publisher Institute of Mathematical Statistics en_US dc.relation.isversionof doi://10.1214/10-AIHP388 en_US dc.relation.hasversion http://arxiv.org/abs/0911.3687v5 en_US dash.license OAP dc.subject random matrix en_US dc.subject sample covariance matrix en_US dc.subject Wishart matrix en_US dc.subject Wigner–Dyson statistics en_US dc.title The local relaxation flow approach to universality of the local statistics for random matrices en_US dc.type Journal Article en_US dc.description.version Accepted Manuscript en_US dc.relation.journal Ann. Inst. H. Poincaré Probab. Statist. en_US dash.depositing.author Yau, Horng-Tzer dc.date.available 2016-02-17T21:32:42Z dc.identifier.doi 10.1214/10-AIHP388 * dash.contributor.affiliated Yau, Horng-Tzer
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