THE DISTRIBUTION OF THE FIRST EIGENVALUE SPACING AT THE HARD EDGE OF THE LAGUERRE UNITARY ENSEMBLE

DOI Web Site 被引用文献2件 参考文献28件

書誌事項

公開日
2007
DOI
  • 10.2206/kyushujm.61.457
公開者
九州大学大学院数理学研究院

この論文をさがす

説明

The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite rank random matrices is found in terms of a Painlevé V system, and the solution of its associated linear isomonodromic system. In particular, it is characterized by the polynomial solutions to the isomonodromic equations which are also orthogonal with respect to a deformation of the Laguerre weight. In the scaling to the hard edge regime we find an analogous situation where a certain Painlevé III' system and its associated linear isomonodromic system characterize the scaled distribution. We undertake extensive analytical studies of this system and use this knowledge to accurately compute the distribution and its moments for various values of the parameter a. In particular, choosing a = ±1/2 allows the first eigenvalue spacing distribution for random real orthogonal matrices to be computed.

収録刊行物

  • 九州数学雑誌

    九州数学雑誌 61 (2), 457-526, 2007

    九州大学大学院数理学研究院

被引用文献 (2)*注記

もっと見る

参考文献 (28)*注記

もっと見る

キーワード

詳細情報 詳細情報について

問題の指摘

ページトップへ