Differential equations for deformed Laguerre polynomials

JOURNAL OF APPROXIMATION THEORY

卷:162

Article

Forrester, Peter J.¹  Ormerod, Christopher M.¹ 

[1] Univ Melbourne, Dept Math & Stat, Parkville, Vic 3010, Australia

关键词: Orthogonal polynomials;    Painleve equations;    Isomonodromy;    Ladder operators;   

DOI  :  10.1016/j.jat.2009.07.010

来源: Elsevier

【 摘 要 】

The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite size may be expressed in terms of a solution of the fifth Painleve transcendent. The generating function of a certain discontinuous linear statistic of the Laguerre unitary ensemble can similarly be expressed in terms of a solution of the fifth Painleve equation. The methodology used to derive these results rely on two theories regarding differential equations for orthogonal polynomial systems, one involving isomonodromic deformations and the other ladder operators. We compare the two theories by showing how either can be used to obtain a characterization of a more general Laguerre unitary ensemble average in terms of the Hamiltonian system for Painleve V. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free