  In previous works, we showed that the internal DLA cluster on \Z^d with t
particles is a.s. spherical up to a maximal error of O(\log t) if d=2 and
O(\sqrt{\log t}) if d > 2. This paper addresses "average error": in a certain
sense, the average deviation of internal DLA from its mean shape is of constant
order when d=2 and of order r^{1-d/2} (for a radius r cluster) in general.
Appropriately normalized, the fluctuations (taken over time and space) scale to
a variant of the Gaussian free field.
