Comment on "Models of intermediate spectral statistics"

Abstract

In this Comment we point out that the semi-Poisson is well suited only as a reference point for the so-called "intermediate statistics," which cannot be interpreted as a universal ensemble, like the Gaussian orthogonal ensemble or the Poissonian statistics. In Ref. [2] it was proposed that the nearest-neighbor distribution P(s) of the spectrum of a Poissonian distributed matrix perturbed by a rank one matrix is similar to the semi-Poisson distribution. We show, however, that the P(s) of this model differs considerably in many aspects from the semi-Poisson. In addition, we give an asymptotic formula for P(s) as s-->0, which gives P'(0) = pi root3/2 for the slope at s = 0. This is different not only from the GOE case, but also from the semi-Poisson prediction.