Asymptotics of discrete β-corners processes via discrete loop equations

We introduce and study stochastic particle ensembles which are natural discretizations of general β-corners processes. We prove that under technical assumptions on a general analytic potential the global fluctuations for the difference between two adjacent levels are asymptotically Gaussian. The covariance is universal and remarkably differs from its counterpart in random matrix theory. Our main tools are certain novel algebraic identities that are multi-level analogues of the discrete loop equations. Based on joint work with Evgeni Dimitrov (Columbia University)