  We examine statistical fluctuation of eigenvalues from the near-edge bulk of
QCD Dirac spectra above the critical temperature. For completeness we start by
reviewing on the spectral property of Anderson tight-binding Hamiltonians as
described by nonlinear sigma models and random matrices, and on the
scale-invariant intermediate spectral statistics at the mobility edge. By
fitting the level spacing distributions, deformed random matrix ensembles which
model multifractality of the wave functions typical of the Anderson
localization transition, are shown to provide an excellent effective
description for such a critical statistics. Next we carry over the above
strategy for the Anderson Hamiltonians to the Dirac spectra. For the staggered
Dirac operators of QCD with 2+1 flavors of dynamical quarks at the physical
point and of SU(2) quenched gauge theory, we identify the precise location of
the mobility edge as the scale-invariant fixed point of the level spacing
distribution. The eigenvalues around the mobility edge are shown to obey
critical statistics described by the aforementioned deformed random matrix
ensembles of unitary and symplectic classes. The best-fitting deformation
parameter for QCD at the physical point turns out to be consistent with the
Anderson Hamiltonian in the unitary class. Finally, we propose a method of
locating the mobility edge at the origin of QCD Dirac spectrum around the
critical temperature, by the use of individual eigenvalue distributions of
deformed chiral random matrices.
