**Abstract:** | In this talk, we study an anisotropic variant of the Kardar-Parisi-Zhang equation, the Anisotropic KPZ equation (AKPZ), in the critical spatial dimension d=2. This is a singular SPDE which is relevant in the description of the time evolution of random surface growth but whose mathematical analysis falls outside of the scope not only of classical stochastic calculus but also of the theory of Regularity Structures and paracontrolled calculus. We consider a regularised version of the AKPZ equation which preserves the invariant measure and show that, contrary to the folklore belief, its solution is logarithmically super-diffusive at large scales. The result is based on the analysis of the generator of the solution of the AKPZ and Wiener chaos analysis. The talk is based on joint works with D. Erhard, P. Sch?nbauer and F. Toninelli. |