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Asymptotics of discrete
$\beta$-corners processes via two-level discrete loop
equations
Evgeni Dimitrov and Alisa Knizel |
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Vol. 3 (2022), No. 2, 247–342
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Abstract |
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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 multilevel analogues of loop equations. |
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Keywords
loop equations, log-gases, corners process
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Mathematical Subject Classification
Primary: 82C41
Secondary: 33D45, 52C20
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Milestones
Received: 30 August 2020
Revised: 10 January 2022
Accepted: 15 February 2022
Published: 8 July 2022
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Authors |
| Evgeni Dimitrov | |
| Department of Mathematics Columbia University New York, NY United States |
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| Alisa Knizel | |
| Department of Statistics University of Chicago Chicago, IL United States |
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