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

2007/06/06 by Peche, Sandrine, Soshnikov, Alexander · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0706.0748

Abstract

We show that the spectral radius of an N× N random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from below by 2 \*σ- o(N^-6/11+ε), where σ² is the variance of the matrix entries and ε is an arbitrary small positive number. Combining with our previous result from [7], this proves that for any ε>0, one has ‖A_N‖ =2 \*σ+ o(N^-6/11+ε) with probability going to 1 as N → ∞.

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