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

Mesoscopic fluctuations of the local density of states in interacting electron systems