Macdonald-Level Extension of Beta Ensembles and Large-N Limit Transition

We introduce and study a family of ( q ,  t )-deformed discrete N -particle beta ensembles, where q and t are the parameters of Macdonald polynomials. The main result is the existence of a large- N limit transition leading to random point processes with infinitely many particles.

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Bibliographic Details
Published in:Communications in mathematical physics 2021-07, Vol.385 (1), p.595-631
Main Author: Olshanski, Grigori
Format: Article
Language:English
Subjects:
Beta rays
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Polynomials
Quantum Physics
Relativity Theory
Theoretical
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Description
Summary:We introduce and study a family of ( q ,  t )-deformed discrete N -particle beta ensembles, where q and t are the parameters of Macdonald polynomials. The main result is the existence of a large- N limit transition leading to random point processes with infinitely many particles.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-020-03899-7