2020
DOI: 10.48550/arxiv.2007.06264
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Macdonald-level extension of beta ensembles and large-N limit transition

Grigori Olshanski

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. Contents( • ; q, t, s) 3.2. Koornwinder polynomials 3.3. Multivariable big q-Jacobi polynomials ϕ λ|N ( • ; q, t; a, b, c, d) 4. One-particle hypergeometric ensembles 5. N-particle hypergeometric ensembles Key words and phrases. Beta-ensem… Show more

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