On the lower bound of the spectral norm of symmetric random matrices with independent entries
Sandrine Peche, Institut Fourier, Grenoble, France
Alexander Soshnikov, University of California at Davis, USA
Abstract
We show that the spectral radius of an N-dimensional random symmetric matrix with i.i.d. bounded centered but non-symmetrically
distributed entries is bounded from below by 2σ - o(N-6/11+ε), where σ2 is the the variance of the matrix entries and ε > 0 is an arbitrary small positive number. Combining with our previous result from [7], this proves
that for any ε > 0 one has ||AN|| = 2σ + o(N-6/11+ε)
with probability going to 1 as N goes to infinity.
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