I am currently learning about lattice-based cryptography and, reading from A Decade of Lattice Cryptography by Peikert, specifically section 2.3, it emerges that
[...] if the parameter s is greater or equal than the smoothing parameter of a lattice, then the sum of independent discrete gaussians (over that lattice) is a discrete gaussian itself.
I am looking for the formal statement (and proof) of that fact without any success. Is anyone able to point me to the appropriate reference?
EDIT: added link to the paper