  This paper is devoted to the statistics of the quantum eigenfunctions in an
ensemble of finite disordered systems (metallic grains). We focus on moments of
inverse participation ratio. In the universal random matrix limit that
corresponds to the infinite conductance of the grains, these moments are
self-averaging quantities. At large but finite conductance the moments do
fluctuate due to the long range correlations in the eigenfunctions. We evaluate
the distributions of fluctuations at given conductance and geometry of the
grains and express them through the spectrum of the diffusion operator in the
grain.
