Random matrix theory (RMT) is used to model the asymptotics of the discrete moments of the derivative of the Riemann zeta function, ζ(s), evaluated at the complex zeros 1/2 + iγ n, using the methods introduced by Keating and Snaith in [14]. We also discuss the probability distribution of In |ζ(1/2 + iγ n)|, proving the central limit theorem for the corresponding random matrix distribution and analysing its large deviations.
