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Wigner random matrices with non-symmetrically distributed entries

Sandrine Peche·Alexander Soshnikov
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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 above by $ 2 \*σ+ o(N^{-6/11+ε}), $ where $σ^2 $ is the variance of the matrix entries and $ε$ is an arbitrary small positive number. Our bound improves the earlier results by Z.Füredi and J.Komlós (1981), and the recent bound obtained by Van Vu (2005).

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Sandrine Peche, Alexander Soshnikov. 2007-04-06. Wigner random matrices with non-symmetrically distributed entries. https://arxiv.org/abs/math/0702035

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