This seminar will be presented in hybrid mode.  The speaker will deliver his talk remotely.

Title: The anisotropic KPZ equation in 2 dimensions

Abstract: The AKPZ equation (a singular, critical SPDE) is a version of the 2-dimensional KPZ SPDE, whose invariant measure is the Gaussian Free Field. We prove that non-linearity of the equation induces logarithmic corrections to diffusivity, namely that the diffusion coefficient diverges in the long-time regime like \sqrt{log t} (for the linear equation, the diffusion coefficient is constant). Secondly, we study the stationary AKPZ equation in the weak-nonlinearity regime and we prove convergence to the stochastic heat equation with additive noise (and finitely renormalized coefficients), for all values of the coupling constant. This is in contrast with the weak-nonlinearity regime of the usual 2d KPZ equation, which undergoes a transition at a finite critical value of the coupling constant.

Joint work with Giuseppe Cannizzaro and Dirk Erhard.

The talk will be followed by refreshments in the Huxley Common Room at 5pm.