Wigner random matrices with non-symmetrically distributed entries

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).

to appear in the Special Issue on Random Matrices of the Journal of Statistical Physics