# Oscillatory Breuer-Major theorem with application to the random corrector problem

## TL;DR

This paper introduces an oscillatory version of the Breuer-Major theorem motivated by the random corrector problem, leading to new insights into Gaussian fluctuations and a variant involving homogeneous measures.

## Contribution

It develops an oscillatory Breuer-Major theorem and applies it to analyze Gaussian fluctuations in the random corrector problem, including a new variant with homogeneous measures.

## Key findings

- Proves an oscillatory Breuer-Major theorem.
- Establishes Gaussian fluctuation results for the random corrector.
- Provides a variant involving homogeneous measures.

## Abstract

In this paper, we present an oscillatory version of the celebrated Breuer-Major theorem that is motivated by the random corrector problem. As an application, we are able to prove new results concerning the Gaussian fluctuation of the random corrector. We also provide a variant of this theorem involving homogeneous measures.