Mathematics Colloquia and Seminars
Non-Equilibrium KPZ from Long-Range InteractionsMathematical Physics & Probability
|Speaker:||Kevin Yang, Stanford University|
|Start time:||Wed, Dec 5 2018, 3:10PM|
The weak KPZ universality asserts that the fluctuations of many random interfaces are governed by the KPZ equation, roughly speaking. In this talk, we discuss this problem for particle systems with long-range interactions. For wedge initial data, this universality result was proved in Dembo-Tsai in 2016 for range at most 3 via the Cole-Hopf method. For stationary initial data, convergence of a "discrete-gradient" of the height profiles to KPZ is a result of Goncalves-Jara in 2016 whose proof is based in the method of energy solutions. We derive the convergence for the same systems in G-J's paper with flat initial data. The idea is to construct a sequence of "equilibrium approximations” via energy solutions and then study the resulting sequence of KPZ/energy solutions with PDE-type arguments.