We analyze the distribution of ∑ m i=1 vixi where x1, . . . ,xm are fixed vectors from some lattice L ⊂ R (say Z) and v1, . . . , vm are chosen independently from a discrete Gaussian distribution over Z. We show that under a natural constraint on x1, . . . ,xm, if the vi are chosen from a wide enough Gaussian, the sum is statistically close to a discrete Gaussian over L. We also analyze the cas...