  A fast method is developed for calculating the Random-Phase-Approximation
(RPA) correlation energy for density functional theory. The correlation energy
is given by a trace over a projected RPA response matrix and the trace is taken
by a stochastic approach using random perturbation vectors. The method scales,
at most, quadratically with the system size but in practice, due to
self-averaging, requires less statistical sampling as the system grows and the
performance is close to linear scaling. We demonstrate the method by
calculating the RPA correlation energy for cadmium selenide and silicon
nanocrystals with over 1500 electrons. In contrast to 2nd order
M{\o}ller-Plesset correlation energies, we find that the RPA correlation
energies per electron are largely independent on the nanocrystal size.
