%0 Journal Article
%T Random sum-free subsets of Abelian groups
%A J¨®zsef Balogh
%A Robert Morris
%A Wojciech Samotij
%J Mathematics
%D 2011
%I arXiv
%X We characterize the structure of maximum-size sum-free subsets of a random subset of an Abelian group $G$. In particular, we determine the threshold $p_c \approx \sqrt{\log n / n}$ above which, with high probability as $|G| \to \infty$, each such subset is contained in a maximum-size sum-free subset of $G$, whenever $q$ divides $|G|$ for some (fixed) prime $q$ with $q \equiv 2 \pmod 3$. Moreover, in the special case $G = \ZZ_{2n}$, we determine a sharp threshold for the above property. The proof uses recent 'transference' theorems of Conlon and Gowers, together with stability theorems for sum-free subsets of Abelian groups.
%U http://arxiv.org/abs/1103.2041v2