Bulk Universality for Wigner Matrices

  title={Bulk Universality for Wigner Matrices},
  author={L{\'a}szl{\'o} Erdős and Jos{\'e} A. Ramı́rez and Benjamin Schlein and H. M.-P. Yau},
We consider N × N Hermitian Wigner random matrices H where the probability density for each matrix element is given by the density ν(x) = e. We prove that the eigenvalue statistics in the bulk is given by Dyson sine kernel provided that U ∈ C(R) with at most polynomially growing derivatives and ν(x) ≤ C e 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… CONTINUE READING
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