Hydrodynamic limits for (2+1)-dimensional interface growth models in the anisotropic KPZ class

par Vincent Lerouvillois

jeudi 15 oct. 2020, 14:00 → 15:00 Europe/Paris

Fokko du Cloux + BBB (ICJ, Bât. Braconnier, Campus La Doua)

Interface growth models are described microscopically by a random discrete height function that evolves according to an irreversible Markovian dynamic (often related to interacting particles systems like ASEP or dimer models). The macroscopic behaviour of the interface is given by the Hydrodynamic limit (Law of Large Numbers) i.e the convergence of the space-time rescaled height function to the solution of a non-linear Hamilton-Jacobi PDE $\partial_t u = v( \nabla u)$. Fluctuations are conjecture to share universal features in link with the KPZ equation, depending on the dimension and the convexity of $v$. I will present the Hydrodynamic limit of the Gates-Westcott model, a (2+1)-dimensional generalisation of the Polynuclear Growth Model in the anisotropic KPZ class and of the Borodin-Ferrari dynamic, a long-jump version of the corner growth model.