Spectral Rigidity and Eigenfunction Correlations at the Anderson   Transition
  The statistics of energy levels for a disordered conductor are considered in the critical energy window near the mobility edge. It is shown that, if critical wave functions are multifractal, the one-dimensional gas of levels on the energy axis is ``compressible'', in the sense that the variance of the level number in an interval is $< (\delta N)^{2} > = \chi <N>$ for $<N> >> 1$. The compressibility, $\chi=\eta/2d$, is given ``exactly'' in terms of the multifractal exponent $\eta=d-D_2$ at the mobility edge in a $d$-dimensional system. 
J. T. Chalker, V. E. Kravtsov, and I. V. Lerner