Asymptotics of discrete $\beta$-corners processes via two-level discrete loop equations

Abstract

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.

85 pages, 2 figures. Version 3: Simplified many of the computations and arguments in the text. Fixed various typos throughout the text

References in corpus (2)

• Fluctuations of eigenvalues of matrix models and their applications
• Matrix models for multilevel Heckman-Opdam and multivariate Bessel measures

Cited by in corpus (2)

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• Large deviations for discrete $\beta$-ensembles