Macdonald-level extension of beta ensembles and large-N limit transition

Abstract

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.

arXiv commentv2: minor revision in accordance with the reviewer suggestions; section 7 extended; accepted in Commun. Math. Phys. v3: a number of typos fixed; uncited references removed

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Cited by in corpus (1)

• Macdonald polynomials and extended Gelfand-Tsetlin graph