Eigenvectors of Wigner matrices: universality of global fluctuations

Details Eigenvectors of Wigner matrices: universality of global fluctuations Eigenvectors of Wigner matrices: universality of global fluctuations

2011-04-07

arxiv.org/abs/1104.1219v6

Mathematics

Probability

18 pages, 1 figure

Scientific paper

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.

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