English

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

Mathematical Physics 2021-07-01 v3 Combinatorics math.MP Probability Representation Theory

Abstract

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

Keywords

Cite

@article{arxiv.2007.06264,
  title  = {Macdonald-level extension of beta ensembles and large-N limit transition},
  author = {Grigori Olshanski},
  journal= {arXiv preprint arXiv:2007.06264},
  year   = {2021}
}

Comments

v2: 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