  We illustrate a general method for calculating spectral statistics that
combines the universal (Random Matrix Theory limit) and the non-universal
(trace-formula-related) contributions by giving a heuristic derivation of the
three-point correlation function for the zeros of the Riemann zeta function.
The main idea is to construct a generalized Hermitian random matrix ensemble
whose mean eigenvalue density coincides with a large but finite portion of the
actual density of the spectrum or the Riemann zeros. Averaging the random
matrix result over remaining oscillatory terms related, in the case of the zeta
function, to small primes leads to a formula for the three-point correlation
function that is in agreement with results from other heuristic methods. This
provides support for these different methods. The advantage of the approach we
set out here is that it incorporates the determinental structure of the Random
Matrix limit.
