Typical weak and superweak values

Weak values, resulting from the action of an operator on a preselected state when measured after postselection by a different state, can lie outside the spectrum of eigenvalues of the operator: they can be 'superweak'. This phenomenon can be quantified by averaging over an ensemble of the two states, and calculating the probability distribution of the weak values. If there are many eigenvalues, distributed within a finite range, this distribution takes a simple universal generalized lorentzian form, and the 'superweak probablility', of weak values outside the spectrum, can be as large as 1-1/root 2 = 0.293.... By contrast, the familiar expectation values always lie within the spectral range, and their distribution, although approximately gaussian for many eigenvalues, is not universal.