2D Anisotropic KPZ at stationarity
A talk in the Bielefeld Stochastic Afternoon series by
Giuseppe Cannizzaro from University of Warwick
| Abstract: | In this talk, we focus on the two-dimensional anisotropic KPZ (aKPZ) equation, which is a singular stochastic PDE. Due to the wild oscillations of the noise and the quadratic nonlinearity, aKPZ is classically ill-posed. It is not possible to linearise it via the Cole-Hopf transformation and the pathwise techniques for singular SPDEs (the theory of Regularity Structures by M. Hairer or the paracontrolled distributions approach of M. Gubinelli, P. Imkeller, N. Perkowski) are not applicable. In the present work, we consider a regularised version of aKPZ which preserves its invariant measure. We show that in order to have subsequential limits once the regularisation is removed, it is necessary to suitably renormalise its coefficients. Moreover, we prove that, in a suitable scaling regime, any limit point differs from the solution to the linear equation obtained by simply dropping the nonlinearity. This is joint work with D. Erhard and P. Schönbauer available at https://arxiv.org/abs/1907.01530 |