  We review our recent theoretical results for mesoscopic fluctuations of the
local density of states in the presence of electron-electron interaction. We
focus on the two specific cases: (i) a vicinity of interacting critical point
corresponding to Anderson-Mott transition, and (ii) a vicinity of
non-interacting critical point in the presence of a weak electron-electron
attraction. In both cases strong mesoscopic fluctuations of the local density
of states exist.
