Appears in collection : 2025 IHES Summer School – Statistical Aspects of Nonlinear Physics

In a system of many particles diffusing in a common environment, the first few particles often have outsized importance. How do they behave and what does that behavior tell us about the environment in which they have evolved? We will approach these problems by studying random walks in random environments and utilizing a connection with the Kardar-Parisi-Zhang stochastic PDE and universality class. I will describe recent work which uncovers new power-laws beyond those of Einstein's theory of diffusion and introduces the Extreme Diffusion Coefficient that captures new microscopic information about the environment.