Edwards-Wilkinson fluctuations in subcritical 2D stochastic heat equations

TL;DR

This paper demonstrates that solutions to certain 2D stochastic heat equations exhibit Edwards-Wilkinson fluctuations under a specific noise limit, extending previous results and showing universality of these fluctuations.

Contribution

It extends prior work by establishing Edwards-Wilkinson fluctuations under weaker coupling conditions and proves the universality of these fluctuations regardless of model specifics.

Findings

Solutions show Edwards-Wilkinson fluctuations asymptotically.

Part of the fluctuations are measurable with respect to the original noise.

Fluctuation statistics are universal, independent of model details.

Abstract

We study 2D nonlinear stochastic heat equations under a logarithmically attenuated white-noise limit with subcritical coupling. We show that solutions asymptotically exhibit Edwards-Wilkinson fluctuations. This extends work of Ran Tao, which required a stricter condition on the coupling. Part of the limiting fluctuation is measurable with respect to the original noise and the remainder is independent. We also show that these statistics are universal in the sense that they are independent of the fine details of the model.