  We introduce and study a class of discrete particle ensembles that naturally
arise in connection with classical random matrix ensembles, log-gases and Jack
polynomials. Under technical assumptions on a general analytic potential we
prove that the global fluctuations of these ensembles are asymptotically
Gaussian with a universal covariance that remarkably differs from its
counterpart in random matrix theory. Our main tools are certain novel algebraic
identities that we have discovered. They play a role of discrete multi-level
analogues of loop equations.
