Dynamical fluctuations in an exactly solvable model of spin glasses

In this paper we calculate the dynamical fluctuations to O(1/N) in the low-temperature phase of the p = 2 spherical spin-glass model. We study the long-time asymptotic regimes and we find, in a short-time-difference regime, a fluctuation dissipation relation for the four-point correlation functions. This relation can be extended to the non-equilibrium regimes introducing a function X_t which, for time t large, varies as t ^-1/2 as in the case of the two-point functions.