Bulk universality for deformed Wigner matrices

We consider N× N random matrices of the form $H=W+V$ where W is a real symmetric or complex Hermitian Wigner matrix and V is a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W, and we choose V so that the eigenvalues of W and V are typically of the same order. For a large class of diagonal matrices V, we show that the local statistics in the bulk of the spectrum are universal in the limit of large N.