Over the last twenty-five years, integrable probability has elucidated universal asymptotic behavior in a host of stochastic systems. By importing and developing new methods that rely on structures like the Yang-Baxter equation and symmetric function theory, researchers have begun to precisely characterize vast universality classes related to stochastic interface growth, interacting particle systems, random walks in random environments, and random tiling models.

The PIs of this targeted Simons research group have been at the forefront of these efforts. Over the duration of this grant, the PIs will build out the theory of universal scaling limits, especially in the presence of non-trivial boundary efforts; as well as broaden their attention to understanding how integrable probability can further be used to unify the study of quantum and classical integrable dynamical systems, both integrable and chaotic. This will include

• Understanding how and why classical integrable systems control the transition probabilities and large deviations for models in integrable probability.
• Proving and expanding beyond physics predictions about the behavior of classical and quantum integrable systems start with random initial data
• Developing the nascent study extreme diffusion by way of studying extreme behavior in random walks in random environments.