Sumsets of random sets

Abstract

Given $m\in \mathbb{N}$ and a $p$-random subset $A\subseteq \mathbb{N}$, we asymptotically determine $\log \mathrm{Pr}(|\mathbb{N}\setminus (A+A)|\ge m)$ for $p$ above the threshold for this property. The proof is based on a bespoke container argument.

15 pages