  We present a generalization of the method of the local relaxation flow to
establish the universality of local spectral statistics of a broad class of
large random matrices. We show that the local distribution of the eigenvalues
coincides with the local statistics of the corresponding Gaussian ensemble
provided the distribution of the individual matrix element is smooth and the
eigenvalues ${x_j}_{j=1}^N$ are close to their classical location
${\gamma_j}_{j=1}^N$ determined by the limiting density of eigenvalues. Under
the scaling where the typical distance between neighboring eigenvalues is of
order 1/N, the necessary apriori estimate on the location of eigenvalues
requires only to know that $\E |x_j - \gamma_j |^2 \le N^{-1-\e}$ on average.
This information can be obtained by well established methods for various matrix
ensembles. We demonstrate the method by proving local spectral universality for
Wishart matrices.
