  We use a standard Monte-Carlo algorithm to study the slow dynamics of a
binary Lennard-Jones glass-forming mixture at low temperature. We find that
Monte-Carlo is by far the most efficient way to simulate a stochastic dynamics
since relaxation is about 10 times faster than in Brownian Dynamics and about
30 times faster than in Stochastic Dynamics. Moreover, the average dynamical
behaviour of the system is in quantitative agreement with the one obtained
using Newtonian dynamics, apart at very short times where thermal vibrations
are suppressed. We show, however, that dynamic fluctuations quantified by
four-point dynamic susceptibilities do retain a dependence on the microscopic
dynamics, as recently predicted theoretically.
