  We prove that an n by n random matrix G with independent entries is
completely delocalized. Suppose the entries of G have zero means, variances
uniformly bounded below, and a uniform tail decay of exponential type. Then
with high probability all unit eigenvectors of G have all coordinates of
magnitude O(n^{-1/2}), modulo logarithmic corrections. This comes a consequence
of a new, geometric, approach to delocalization for random matrices.
