# Convergence rates in the central limit theorem for weighted sums of Bernoulli random fields

## TL;DR

This paper establishes convergence rates in the central limit theorem for weighted sums of Bernoulli random fields by deriving moment inequalities and using approximation techniques.

## Contribution

It introduces new moment inequalities for functionals of i.i.d. random fields and provides explicit convergence rates for weighted sums of Bernoulli random fields.

## Key findings

- Derived moment inequalities for functionals of i.i.d. random fields
- Established convergence rates in the CLT for weighted sums of Bernoulli random fields
- Used approximation by m-dependent random fields to achieve results

## Abstract

We prove moment inequalities for a class of functionals of i.i.d. random fields. We then derive rates in the central limit theorem for weighted sums of such randoms fields via an approximation by $m$-dependent random fields.