  Let $U_n=[u_{i,j}]$ be the eigenvectors matrix of a Wigner matrix. We prove
that under some moments conditions, the bivariate random process indexed by
$[0,1]^2$ with value at $(s,t)$ equal to the sum, over $1\le i \le ns$ and
$1\le j \le nt$, of $|u_{i,j}|^2 - 1/n$, converges in distribution to the
bivariate Brownian bridge. This result has already been proved for GOE and GUE
matrices. It is conjectured here that the necessary and sufficient condition,
for the result to be true for a general Wigner matrix, is the matching of the
moments of orders 1, 2 and 4 of the entries of the Wigner with the ones of a
GOE or GUE matrix. Surprisingly, the third moment of the entries of the Wigner
matrix has no influence on the limit distribution.
