We study Ostwald ripening in the regime of small volume fraction and consider spatially periodic systems whose size is smaller than the screening length. Within the snapshot perspective we obtain an explicit characterization of the leading-order deviation to the classical mean-field theory by Lifshitz, Slyozov and Wagner (LSW). Using this representation, we show that the corrections are not universal, in the sense that the mean value has a strong dependence on geometry, and arbitrarily large fluctuations can happen with finite probability.