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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2019
- DOI:
- 10.48550/arXiv.1905.02338
- arXiv:
- arXiv:1905.02338
- Bibcode:
- 2019arXiv190502338D
- Keywords:
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- Mathematics - Probability;
- Mathematical Physics;
- 82C41;
- 33D45;
- 52C20
- E-Print:
- 85 pages, 2 figures. Version 3: Simplified many of the computations and arguments in the text. Fixed various typos throughout the text