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This article is a contribution to the understanding of fluctuations in theout of equilibrium dynamics of glassy systems. By extending theoretical ideasbased on the assumption that time-reparametrization invariance developsasymptotically we deduce the scaling properties of diverse high-ordercorrelation functions. We examine these predictions with numerical tests in astandard glassy model, the 3d Edwards-Anderson spin-glass, and in a systemwhere time-reparametrization invariance is not expected to hold, the 2dferromagnetic Ising model, both at low temperatures. Our results enlighten aqualitative difference between the fluctuation properties of the two models andshow that scaling properties conform to the time-reparametrization invariancescenario in the former but not in the latter.

Fluctuations of two-time quantities and time-reparametrization invariance in spin-glasses