Abelian Groups Are Polynomially Stable

In recent years, there has been a considerable amount of interest in stability of equations and their corresponding groups. Here, we initiate the systematic study of the quantitative aspect of this theory. We develop a novel method, inspired by the Ornstein–Weiss quasi-tiling technique, to prove that abelian groups are polynomially stable with respect to permutations, under the normalized Hamming ...