  We show that the Dyson Brownian Motion exhibits local universality after a
very short time assuming that local rigidity and level repulsion hold. These
conditions are verified, hence bulk spectral universality is proven, for a
large class of Wigner-like matrices, including deformed Wigner ensembles and
ensembles with non-stochastic variance matrices whose limiting densities differ
from the Wigner semicircle law.
