Equivalence of Fluctuations Between SHE and KPZ Equation in Weak Disorder Regime
Explore the connection between the stochastic heat equation (SHE) and the Kardar-Parisi-Zhang (KPZ) equation in this 50-minute lecture by Shuta Nakajima from Meiji University. Delve into the challenges of constructing solutions to the KPZ equation, a fundamental model in non-equilibrium statistical physics that describes the random evolution of interfaces. Learn about the rigorous demonstration of the equivalence of fluctuations between SHE and KPZ equation in the weak disorder regime for three and higher dimensions. Gain insights into this enduring open problem, particularly in finding solutions in two and higher dimensions. The lecture, presented at the Institut des Hautes Etudes Scientifiques (IHES), is based on joint work with Stefan Junk from Gakushuin University.