کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4607615 | 1337873 | 2010 | 25 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Differential equations for deformed Laguerre polynomials Differential equations for deformed Laguerre polynomials](/preview/png/4607615.png)
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 Painlevé 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 Painlevé 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 Painlevé V.
Journal: Journal of Approximation Theory - Volume 162, Issue 4, April 2010, Pages 653–677