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

journal of physics. a, mathematical and theoretical

A method for calculating spectral statistics based on random-matrix  universality with an application to the three-point correlations of the  Riemann zeros