  We consider the initial energy density in the transverse plane of a high
energy nucleus-nucleus collision as a random field $\rho(\x)$, whose
probability distribution $P[\rho]$, the only ingredient of the present
description, encodes all possible sources of fluctuations. We argue that it is
a local Gaussian, with a short-range 2-point function, and that the
fluctuations relevant for the calculation of the eccentricities that drive the
anisotropic flow have small relative amplitudes. In fact, this 2-point
function, together with the average density, contains all the information
needed to calculate the eccentricities and their variances, and we derive
general model independent expressions for these quantities. The short
wavelength fluctuations are shown to play no role in these calculations, except
for a renormalization of the short range part of the 2-point function. As an
illustration, we compare to a commonly used model of independent sources, and
recover the known results of this model.
