Gaussian fluctuations of a nonlinear stochastic heat equation in dimension two

We study the Gaussian fluctuations of a nonlinear stochastic heat equation in spatial dimension two. The equation is driven by a Gaussian multiplicative noise. The noise is white in time, smoothed in space at scale epsilon, and tuned logarithmically by a factor 1/root log epsilon(-1)in its strength. We prove that, after centering and rescaling, the solution 1 random field converges in distribution to an Edwards-Wilkinson limit as epsilon down arrow 0. The tool we used here is the Malliavin-Stein's method. We also give a functional version of this result.