  We study theoretically the spontaneous emission from an inhomogeneous
ensemble of quantum dots in the weak excitation limit. We show that collective,
superradiance-like effects lead to an enhanced emission rate in the presence of
sufficiently strong coupling between the dots in agreement with experimental
observations, which means that the quantum dot sample cannot be treated as an
ensemble of individual emitters. We demonstrate also that the collective
behavior of the quantum dot system relies on short-range interactions, while
long-range dipole couplings are too weak to have any impact on the emission
dynamics for a system with a realistic degree of inhomogeneity.
