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A note on the Central Limit Theorem for the Eigenvalue Counting Function of Wigner Matrices

   
@article{ECP1634,
	author = {Sandrine Dallaporta and Van Vu},
	title = {A note on the Central Limit Theorem for the Eigenvalue Counting Function of Wigner Matrices},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {16},
	year = {2011},
	keywords = {random matrices ; eigenvalue counting function ; Central Limit Theorem ; Four Moment Theorem ; localization},
	abstract = {The purpose of this note is to establish a Central Limit Theorem for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on the correct asymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson, and its extension to large families of Wigner matrices by means of the Tao and Vu Four Moment Theorem and recent localization results by Erd?s, Yau and Yin.},
	pages = {no. 30, 214-322},
	issn = {1083-589X},
	doi = {10.1214/ECP.v16-1634},    
        url = {http://ecp.ejpecp.org/article/view/1634}}