  Liquids near the glass transition exhibit dynamical heterogeneity, i.e.
correlated regions in the liquid relax at either a much faster rate or a much
slower rate than the average. This is a collective phenomenon that has been
characterized by measurements that attempt to determine the size of these
regions and the intensity of the fluctuations. Here we show that the results of
those measurements can be affected not only by the collective fluctuations in
the relaxation rate, but also by density fluctuations in the initial state and
by single-particle fluctuations, which can become dominant for very long
timescales. We introduce a method to subtract the effect of those extra
fluctuations, and apply it to numerical simulations of two glass forming
models: a binary hard sphere system and a Kob-Andersen Lennard-Jones system.
This method allows us to extend the analysis of numerical data to timescales
much longer than previously possible, and opens the door for further future
progress in the study of dynamic heterogeneities, including the determination
of the exchange time.
