# Fluctuations of the solutions to the KPZ equation in dimensions three and higher

## TL;DR

This paper proves that in three or more dimensions, the large-scale fluctuations of the KPZ equation with small coupling are described by the Edwards-Wilkinson model, using probabilistic techniques on Wiener space.

## Contribution

It provides an alternative proof, avoiding perturbation expansions, that the KPZ fluctuations in higher dimensions are governed by the Edwards-Wilkinson model.

## Key findings

- KPZ fluctuations in d≥3 match Edwards-Wilkinson model
- Uses probabilistic techniques on Wiener space
- Avoids perturbation expansion methods

## Abstract

We prove, using probabilistic techniques and analysis on the Wiener space, that the large scale fluctuations of the KPZ equation in $d\geq 3$ with a small coupling constant, driven by a white in time and colored in space noise, are given by the Edwards-Wilkinson model. This gives an alternative proof, that avoids perturbation expansions, to the results of Magnen and Unterberger \cite{magnen2017diffusive}.