Statistics of Rare Events in Disordered Conductors

Asymptotic behavior of distribution functions of local quantities in disordered conductors is studied in the weak disorder limit by means of an optimal fluctuation method. It is argued that this method is more appropriate for the study of seldom occurring events than the approaches based on nonlinear $\sigma$-models because it is capable of correctly handling fluctuations of the random potential with large amplitude as well as the short-scale structure of the corresponding solutions of the Schr\"{o}dinger equation. For two- and three-dimensional conductors new asymptotics of the distribution functions are obtained which in some cases differ significantly from previously established results.