Asymptotics of discrete $\beta$corners processes via twolevel discrete loop equations
Abstract
We introduce and study stochastic particle ensembles which are natural discretizations of general $\beta$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 twolevel analogues of the discrete loop equations.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.02338
 Bibcode:
 2019arXiv190502338D
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 82C41;
 33D45;
 52C20
 EPrint:
 102 pages, 2 figures. Fixed a typo in v1 that propagated all the way to the main result  Theorem 1.7 (Theorem 1.9 in v1). Assumption 6 in Section 3 has been removed and Assumption 5 relaxed. A new appendix has been added. Several applications have been added in Section 6 (Section 7 in v1). In Section 7 (Section 6 in v1) the restriction $\theta \geq 1$ has been relaxed to $\theta >