# The central limit theorem for Riesz-Raikov sums II

## TL;DR

This paper proves a central limit theorem for sums of periodic functions evaluated along sequences generated by expanding matrices, extending understanding of their probabilistic behavior.

## Contribution

It establishes the CLT for Riesz-Raikov sums involving expanding matrices, advancing the theory for multidimensional dynamical systems.

## Key findings

- Proves CLT for sums of periodic functions along matrix orbits
- Extends previous results to multidimensional expanding matrices
- Provides conditions under which the CLT holds

## Abstract

For a $d\times d$ expanding matrix $A$, we investigate randomness of the sequence $\{A^k x\}$ and prove the central limit theorem for $\sum f(A^k x)$ where $f$ is a periodic function with a mild regularity condition.