Prof. Giuseppe Cannizzaro gave a lecture titled “Logarithmic Super-diffusivity for the 2-dimensional Stationary Anisotropic KPZ” at AMSS on April 14, 2012.
In this talk, they studied an anisotropic variant of the Kardar-Parisi-Zhang equation, the Anisotropic KPZ equation (AKPZ), in the critical spatial dimension d=2. This was a singular SPDE which was relevant in the description of the time evolution of random surface growth but whose mathematical analysis fell outside of the scope not only of classical stochastic calculus but also of the theory of Regularity Structures and paracontrolled calculus. We considered a regularised version of the AKPZ equation which preserved the invariant measure and showed that, contrary to the folklore belief, its solution was logarithmically super-diffusive at large scales. The result was based on the analysis of the generator of the solution of the AKPZ and Wiener chaos analysis.
The talk was based on joint works with D. Erhard, P. Schnbauer and F. Toninelli.