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 -deformed discrete -particle beta ensembles, where and are the parameters of Macdonald polynomials. The main result is the existence of a large- limit transition leading to random point processes with infinitely many particles.
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