Gap Probabilities in the Laguerre Unitary Ensemble and Discrete Painlev\'e Equations
Exactly Solvable and Integrable Systems
2020-08-20 v2 Mathematical Physics
math.MP
Abstract
In this paper we study a certain recurrence relation, that can be used to generate ladder operators for the Laguerre Unitary ensemble, from the point of view of Sakai's geometric theory of Painlev\'e equations. On one hand, this gives us one more detailed example of the appearance of discrete Painlev\'e equations in the theory of orthogonal polynomials. On the other hand, it serves as a good illustration of the effectiveness of a recently proposed procedure on how to reduce such recurrences to some canonical discrete Painlev\'e equations.
Keywords
Cite
@article{arxiv.2001.00494,
title = {Gap Probabilities in the Laguerre Unitary Ensemble and Discrete Painlev\'e Equations},
author = {Yang Chen and Anton Dzhamay and Jie Hu},
journal= {arXiv preprint arXiv:2001.00494},
year = {2020}
}
Comments
16 pages. arXiv admin note: text overlap with arXiv:1910.10981