@article{2837,
abstract = {We consider a general class of N × N random matrices whose entries hij are independent up to a symmetry constraint, but not necessarily identically distributed. Our main result is a local semicircle law which improves previous results [17] both in the bulk and at the edge. The error bounds are given in terms of the basic small parameter of the model, maxi,j E|hij|2. As a consequence, we prove the universality of the local n-point correlation functions in the bulk spectrum for a class of matrices whose entries do not have comparable variances, including random band matrices with band width W ≫N1-εn with some εn > 0 and with a negligible mean-field component. In addition, we provide a coherent and pedagogical proof of the local semicircle law, streamlining and strengthening previous arguments from [17, 19, 6].},
author = {Erdös, László and Knowles, Antti and Yau, Horng and Yin, Jun},
journal = {Electronic Journal of Probability},
number = {59},
pages = {1--58},
publisher = {Institute of Mathematical Statistics},
title = {{The local semicircle law for a general class of random matrices}},
doi = {10.1214/EJP.v18-2473},
volume = {18},
year = {2013},
}