Comment by krnsll

Not at all, the proof was a very elegant argument involving fourier transforms and an integral estimate going back to the study of controlling random walks (Khintchine's inequality). I say elegant in the manner of it being enviably so -- a proof a beginning graduate student could follow while capturing a fundamental, easy to state fact.

This work does however situate itself in/adjacent to that broad space of Brunn-Minkowski theory.