Appears in collection : French Japanese Conference on Probability and Interactions

I will The Kardar-Parisi-Zhang (KPZ) equation is a mathematical model that describes the random evolution of interfaces. The equation has become a fundamental model in non-equilibrium statistical physics. Constructing a solution to the KPZ equation in any dimension presents a significant challenge due to its inherent non-linearity. This challenge has resulted in an enduring open problem, particularly in finding solutions in two and higher dimensions. This talk will explore the intriguing connection between the stochastic heat equation (SHE) and the KPZ equation. It offers a rigorous demonstration of the equivalence of fluctuations in these systems in the weak disorder regime for three and higher dimensions. This talk is based on joint work with Stefan Junk (Gakushuin University).