A fundamental property of GinOE is that away from the real axis its statistical properties coincide with GinUE. In keeping with this, the limiting variance formula is found to the be the same as for GinUE. Also, the Coulomb gas interpretation of the eigenvalue PDF for GinOE implies, that as for GinOE, screening sum rules linking correlation functions hold true. The singular values and eigenvectors both permit studies analogous to those for GinUE, although in the case of the eigenvectors, there is now an advantage in considering the joint probability distribution of the position of the eigenvalue (assumed real) and the invariant overlap.

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Analogues of GinUE Statistical Properties for GinOE

  • Sung-Soo Byun,
  • Peter J. Forrester

摘要

A fundamental property of GinOE is that away from the real axis its statistical properties coincide with GinUE. In keeping with this, the limiting variance formula is found to the be the same as for GinUE. Also, the Coulomb gas interpretation of the eigenvalue PDF for GinOE implies, that as for GinOE, screening sum rules linking correlation functions hold true. The singular values and eigenvectors both permit studies analogous to those for GinUE, although in the case of the eigenvectors, there is now an advantage in considering the joint probability distribution of the position of the eigenvalue (assumed real) and the invariant overlap.