Non-equilibrium Dynamics and Random Matrices

Our goal is to explain how certain basic representation theoretic ideas and constructions encapsulated in the form of Macdonald processes lead to nontrivial asymptotic results in various `integrable'; probabilistic problems. Examples include dimer models, general beta random matrix ensembles, and various members of the \((2+1)d\) anisotropic KPZ and \((1+1)d\) KPZ universality classes, such as growing stepped surfaces, \(q\)-TASEP, \(q\)-PushASEP, and directed polymers in random media. No prior knowledge of the subject will be assumed.