Section: New Results

Towards the weak KPE universality conjecture

In [32], P. Gonçalves, N. Perkowski and M. Simon derive the KPZ equation with boundary conditions, from an interacting particle system in contact with stochastic reservoirs, and they legitimate the choice done at the macroscopic level for the KPZ equation from the microscopic description of the system. This is more subtle than expected, because the boundary conditions do not behave canonically. The main challenge is to clarify the link between the macroscopic boundary effects and their atomic description.