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Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation

   
@article{EJP768,
	author = {Laszlo Erdos and Jose Ramirez and Benjamin Schlein and Horng-Tzer Yau},
	title = {Universality of Sine-Kernel for Wigner Matrices with a Small Gaussian Perturbation},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {15},
	year = {2010},
	keywords = {Wigner random matrix, Dyson sine kernel},
	abstract = {We consider $N\times N$ Hermitian random matrices with independent identically distributed entries (Wigner matrices). We assume that the distribution of the entries have a Gaussian component with variance $N^{-3/4+\beta}$ for some positive $\beta>0$. We prove that the local eigenvalue statistics follows the universal Dyson sine kernel.},
	pages = {no. 18, 526-604},
	issn = {1083-6489},
	doi = {10.1214/EJP.v15-768},    
        url = {http://ejp.ejpecp.org/article/view/768}}