Wigner random matrices with non-symmetrically distributed entries

Details Wigner random matrices with non-symmetrically distributed entries Wigner random matrices with non-symmetrically distributed entries

2007-02-01

arxiv.org/abs/math/0702035v2

Mathematics

Probability

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

Scientific paper

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 \*\sigma + o(N^{-6/11+\epsilon}), $ where $\sigma^2 $ is the variance of the matrix entries and $\epsilon $ is an arbitrary small positive number. Our bound improves the earlier results by Z.F\"{u}redi and J.Koml\'{o}s (1981), and the recent bound obtained by Van Vu (2005).

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