KPZ and Boltzmann-Gibbs Principle
11th May 2022, 4:00 pm – 5:00 pm
Fluctuation theory for hydrodynamic limits of interacting particle systems in (1+1)-dimensions is conjectured to generally be governed by linear and (KPZ) quadratic corrections. Boltzmann-Gibbs principles are supposed to provide a general method of rigorously establishing something of this type. Much is known for stationary systems with sufficiently explicit invariant measures, while little is known for non-stationary systems outside a class of “partially integrable” models such as ASEP. In this talk, we broadly discuss KPZ equation fluctuations for general non-stationary systems. We then specialize to a perturbation of ASEP, where the main problem is deriving the aforementioned linear-type corrections with a method that should extend quite generally.