  This article is a contribution to the understanding of fluctuations in the
out of equilibrium dynamics of glassy systems. By extending theoretical ideas
based on the assumption that time-reparametrization invariance develops
asymptotically we deduce the scaling properties of diverse high-order
correlation functions. We examine these predictions with numerical tests in a
standard glassy model, the 3d Edwards-Anderson spin-glass, and in a system
where time-reparametrization invariance is not expected to hold, the 2d
ferromagnetic Ising model, both at low temperatures. Our results enlighten a
qualitative difference between the fluctuation properties of the two models and
show that scaling properties conform to the time-reparametrization invariance
scenario in the former but not in the latter.
