Gaussian fluctuations of a nonlinear stochastic heat equation in dimension two

Abstract

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 $\frac{1}{\sqrt{\log {\epsilon }^{-1}}}$ in its strength. We prove that, after centering and rescaling, the solution random field converges in distribution to an Edwards-Wilkinson limit as $\epsilon \downarrow 0$. The tool we used here is the Malliavin-Stein's method. We also give a functional version of this result.

References in corpus (5)

• The Edwards-Wilkinson limit of the random heat equation in dimensions three and higher
• On the moments of the (2+1)-dimensional directed polymer and stochastic heat equation in the critical window
• Moments of the 2D SHE at criticality
• Renormalizing the Kardar-Parisi-Zhang equation in $d\ge 3$ in weak disorder
• Averaging Gaussian functionals

Cited by in corpus (2)

• Moments of the 2d directed polymer in the subcritical regime and a generalisation of the Erdös-Taylor theorem
• Mesoscopic averaging of the two-dimensional KPZ equation