Nonconventional moderate deviations theorems and exponential concentration inequalities

TL;DR

This paper develops moderate deviations theorems and exponential concentration inequalities for nonconventional sums involving complex dependencies, extending classical probabilistic bounds to more intricate sum structures.

Contribution

It introduces new moderate deviations results and Bernstein-type inequalities for nonconventional sums, broadening the scope of probabilistic concentration tools.

Findings

Established moderate deviations theorems for nonconventional sums.

Derived exponential concentration inequalities of Bernstein type.

Extended classical results to sums with complex dependency structures.

Abstract

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