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On the lower bound of the spectral norm of symmetric random matrices with independent entries

   
@article{ECP1376,
	author = {Sandrine Peche and Alexander Soshnikov},
	title = {On the lower bound of the spectral norm of symmetric random matrices with independent entries},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {13},
	year = {2008},
	keywords = {Wigner random matrices, spectral norm},
	abstract = {We show that the spectral radius of an $N\times N$ random symmetric matrix with i.i.d. bounded centered but non-symmetrically  distributed entries  is bounded from below by   $ 2 \sigma - o( N^{-6/11+\varepsilon}), $ where $\sigma^2 $ is the variance of the matrix   entries and $\varepsilon $ is an arbitrary small positive number.   Combining with our previous result from [7], this proves   that for any  $\varepsilon >0, \ $ one has  $ \|A_N\| =2 \sigma + o( N^{-6/11+\varepsilon}) $ with probability going to $ 1 $ as $N \to \infty$.},
	pages = {no. 28, 280-290},
	issn = {1083-589X},
	doi = {10.1214/ECP.v13-1376},    
        url = {http://ecp.ejpecp.org/article/view/1376}}