Diagonal approximation of the form factor of the unitary group

The form factor of the unitary group U(N) endowed with the Haar measure characterizes the correlations within the spectrum of a typical unitary matrix. It can be decomposed into a sum over pairs of 'periodic orbits', where by periodic orbit we understand any sequence of matrix indices. From here the diagonal approximation can be defined in the usual fashion as a sum only over pairs of identical orbits. We prove that as we take the dimension N to infinity, the diagonal approximation becomes 'exact', that is converges to the full form factor in the interval τ is an element of [0, 1]. (letter to the editor)