On the Bogolyubov-Ruzsa lemma

Abstract

Our main result is that if A is a finite subset of an abelian group with |A+A| < K|A|, then 2A-2A contains an O(log^{O(1)} K)-dimensional coset progression M of size at least exp(-O(log^{O(1)} K))|A|.

28 pp. Corrected typos. Added appendix on model setting