Nonconventional moderate deviations theorems and exponential concentration inequalities

Abstract

We obtain moderate deviations theorems and exponential (Bernstein type) concentration inequalities for "nonconventional" sums of the form $S_N={\sum }_{n=1}^N(F({\xi }_{q_1(n)},{\xi }_{q_2(n)},...,{\xi }_{q_{\ell }(n)})-\bar{F})$.

24 pages; In the third version Young towers can be considered in Theorems 2.3 and 2.4. In the fourth, a corrected proof of Theorem 6.3 appears. To appear in AIHP