We discuss a recent result which makes early progress towards understanding temperature chaos in the Kardar–Parisi–Zhang universality class. We show that the appropriately centered and scaled free energy of positive temperature Continuum Directed Random Polymers (CDRPs) at distinct temperatures, coupled through the underlying noise, converge jointly to independent directed landscapes in the zero-temperature limit, if the temperatures are sufficiently separated. If time allows, we will also discuss how the same proof idea allows us to show that the directed landscape is a two-dimensional noise, which, combined with earlier work of H.-Parekh, implies that it is a two-dimensional black noise. This is the third known example of a two-dimensional black noise.
This talk is based on joint work with Shirshendu Ganguly and Victor Ginsburg.