--- res: bibo_abstract: - We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with centered independent entries. In contrast to previous works the matrix of variances sij=\mathbbmE|hij|2 is not assumed to be stochastic. Hence the density of states is not the Wigner semicircle law. Its possible shapes are described in the companion paper (Ajanki et al. in Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We show that as N grows, the resolvent, G(z)=(H−z)−1, converges to a diagonal matrix, diag(m(z)), where m(z)=(m1(z),…,mN(z)) solves the vector equation −1/mi(z)=z+∑jsijmj(z) that has been analyzed in Ajanki et al. (Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We prove a local law down to the smallest spectral resolution scale, and bulk universality for both real symmetric and complex hermitian symmetry classes.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Oskari H foaf_name: Ajanki, Oskari H foaf_surname: Ajanki foaf_workInfoHomepage: http://www.librecat.org/personId=36F2FB7E-F248-11E8-B48F-1D18A9856A87 - foaf_Person: foaf_givenName: László foaf_name: Erdös, László foaf_surname: Erdös foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0001-5366-9603 - foaf_Person: foaf_givenName: Torben H foaf_name: Krüger, Torben H foaf_surname: Krüger foaf_workInfoHomepage: http://www.librecat.org/personId=3020C786-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-4821-3297 bibo_doi: 10.1007/s00440-016-0740-2 bibo_issue: 3-4 bibo_volume: 169 dct_date: 2017^xs_gYear dct_identifier: - UT:000414358400002 dct_isPartOf: - http://id.crossref.org/issn/01788051 dct_language: eng dct_publisher: Springer@ dct_title: Universality for general Wigner-type matrices@ ...