 0981 Laszlo Erdos, Jose A. Ramirez, Benjamin Schlein, HorngTzer Yau
 Bulk Universality for Wigner Matrices
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May 26, 09

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Abstract. We consider $N\times N$ Hermitian Wigner random matrices
$H$ where the probability density
for each matrix element is given by the density $\nu(x)= e^{ U(x)}$.
We prove that the eigenvalue statistics in the bulk is given by
Dyson sine kernel provided that $U \in C^6(\RR)$
with at most polynomially growing derivatives and
$\nu(x) \le C\, e^{  C x}$ for $x$ large.
The proof is based upon an approximate time reversal of
the Dyson Brownian motion combined with the convergence of
the eigenvalue density to the Wigner semicircle law on
short scales.
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