论文标题
Laguerre单一合奏和离散painlevé方程中的差距概率
Gap Probabilities in the Laguerre Unitary Ensemble and Discrete Painlevé Equations
论文作者
论文摘要
在本文中，我们研究了一定的复发关系，可以用来从Sakai的Parelevé方程式几何理论的角度来为Laguerre单一合奏生成梯子操作员。一方面，这为我们提供了一个正交多项式理论中离散painlevé方程式出现的一个详细示例。另一方面，它可以很好地说明最近提出的程序的有效性，即如何将这种复发减少到某些规范离散的Painlevé方程。
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 Painlevé equations. On one hand, this gives us one more detailed example of the appearance of discrete Painlevé 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 Painlevé equations.
