@article{EJP2473,
author = {László Erdős and Antti Knowles and Horng-Tzer Yau and Jun Yin},
title = {The local semicircle law for a general class of random matrices},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {18},
year = {2013},
keywords = {Random band matrix; local semicircle law; universality; eigenvalue rigidity},
abstract = {We consider a general class of $N\times N$ random matrices whose entries $h_{ij}$ are independent up to a symmetry constraint, but not necessarily identically distributed. Our main result is a local semicircle law which improves previous results both in the bulk and at the edge. The error bounds are given in terms of the basic small parameter of the model, $\max_{i,j} \mathbb{E} \left|h_{ij}\right|^2$. 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 $W\gg N^{1-\varepsilon_n}$ with some $\varepsilon_n>0$ 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.},
pages = {no. 59, 1-58},
issn = {1083-6489},
doi = {10.1214/EJP.v18-2473},
url = {http://ejp.ejpecp.org/article/view/2473}}