There is a distinction between the Ginibre ensemble with complex entries (GinUE) and those with real or quaternion entries (GinOE and GinSE, respectively). First, the eigenvalues of GinUE form a determinantal point process, while those of GinOE and GinSE have the more complicated structure of a Pfaffian point process.
Sung-Soo Byun is Assistant Professor in the Department of Mathematical Sciences at Seoul National University. Peter J. Forrester is Professor in School of Mathematics and Statistics at The University of Melbourne.
Introduction.- Eigenvalue PDFs and Correlations.- Fluctuation Formulas.- Coulomb Gas Model, Sum Rules and Asymptotic Behaviours.- Normal Matrix Models.- Further Theory and Applications.- Eigenvalue Statistics for GinOE and Elliptic GinOE.- Analogues of GinUE Statistical Properties for GinOE.- Further Extensions to GinOE.- Statistical Properties of GinSE and Elliptic GinSE.- Further Extensions to GinSE.