Universality for generalized Wigner matrices with Bernoulli distribution

The universality for the eigenvalue spacing statistics of generalized Wigner matrices was established in our previous work A major class of probability measures excluded in In this paper, we extend the universality result of The new ingredient is a strong local semicircle law which improves the error estimate on the Stieltjes transform of the empirical measure of the eigenvalues from the order (N) -1/2 to (N) -1 . Here is the imaginary part of the spectral parameter in the definition of the Stieltjes transform and N is the size of the matrix.