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As for GinUE, GinOE permits a number of related ensembles which share many of its special properties. One of these, already introduced in the previous chapter, is elliptic GinOE. Considered in this chapter are the induced GinOE, which relates to a polar decomposition involving a rectangular generalisation of a GinOE matrix and a random Haar real orthogonal matrix; the real spherical ensemble of matrices \(G_1^{-1} G_2\) , with both \(G_1,G_2\) GinOE matrices; the sub-block of a Haar real orthogonal matrix; and products of GinOE matrices. Common structures and statistical features are emphasised, with again the occurrence of real eigenvalues responsible for topics of study beyond those for GinUE and its extensions.

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Further Extensions to GinOE

  • 章节

  • 出版模式：

    开放获取

  • 发表日期：

    2025年

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  • Sung-Soo Byun,
  • Peter J. Forrester

摘要

As for GinUE, GinOE permits a number of related ensembles which share many of its special properties. One of these, already introduced in the previous chapter, is elliptic GinOE. Considered in this chapter are the induced GinOE, which relates to a polar decomposition involving a rectangular generalisation of a GinOE matrix and a random Haar real orthogonal matrix; the real spherical ensemble of matrices \(G_1^{-1} G_2\) , with both \(G_1,G_2\) GinOE matrices; the sub-block of a Haar real orthogonal matrix; and products of GinOE matrices. Common structures and statistical features are emphasised, with again the occurrence of real eigenvalues responsible for topics of study beyond those for GinUE and its extensions.