December 4, 2015
Location: Drift 21, room 003
The weak KPZ universality conjecture II
The KPZ equation was introduced in the '80s by Kardar, Parisi and Zhang as a simplified model for stochastic growth of one-dimensional interfaces. From heuristic considerations, it has been conjectured that scaling limits of general stationary, non-equilibrium fluctuations of one-dimensional, conservative dynamics are governed by the KPZ equation (the so-called weak KPZ universality conjecture). However, from the mathematical point of view, the KPZ equation is not well posed, and more than 25 years passed until a satisfactory notion of solution was built.
In fact, the celebrated Hairer's theory of regularity structures appeared as a way to make sense of the KPZ equation. An earlier, weaker notion of ‘energy solutions’ of the KPZ equation was introduced in joint works with Massimiliano Gubinelli and Patricia Gonçalves. Very recently, Gubinelli and Perkowski have proved the uniqueness of stationary solutions of the KPZ equation, paving the way to the proof of the weak KPZ universality conjecture.
The aim of this series of lectures is to present a complete proof of the weak KPZ universality conjecture, using the notion of energy solutions of the KPZ equation.
The weak KPZ universality conjecture III
See the abstract of the morning lecture.