# On the normal approximation for random fields via martingale methods

## TL;DR

This paper establishes a central limit theorem for stationary random fields using martingale methods, extending classical results and providing new applications to linear and nonlinear Volterra-type fields.

## Contribution

It introduces a sharp projective condition for CLT in random fields and develops new martingale difference results applicable to various field types.

## Key findings

- Proves CLT under a sharp projective condition for stationary fields.
- Extends results to linear and nonlinear Volterra-type random fields.
- Develops new martingale difference array results.

## Abstract

We prove a central limit theorem for strictly stationary random fields under a sharp projective condition. The assumption was introduced in the setting of random variables by Maxwell and Woodroofe. Our approach is based on new results for triangular arrays of martingale differences, which have interest in themselves. We provide as applications new results for linear random fields and nonlinear random fields of Volterra-type.