Gaussian fluctuations of a nonlinear stochastic heat equation in dimension two (Q6548534)

In this article, the Gaussian fluctuations of a nonlinear stochastic heat equation in spatial dimension two are studied by the author. The equation is driven by a Gaussian multiplicative noise, which is white in time and smoothed in space at scale \( \varepsilon \), with its strength tuned logarithmically by a factor of \( \sqrt{\frac{1}{\log \varepsilon^{-1}}} \). It is proved by the author that, after centering and rescaling, the solution random field converges in distribution to an Edwards-Wilkinson limit as \( \varepsilon \to 0 \). The Malliavin-Stein method is employed as the primary analytical tool. Additionally, a functional version of this result is provided by the author.