Classical random matrix ensembles

Abstract

Introduced first is the classification of the classical GOE, GUE and GSE ensembles. To get started with their properties, nearest neighbor spacing distributions (NNSD) for the simple 2×2 matrix version of these ensembles are derived. Going further, one and two-point functions (in the eigenvalues) for general N×N GOE and GUE are derived using the so called binary correlation approximation. Measures for level fluctuations as given by the number variance and Dyson-Mehta Δ3 statistic on one hand and on the other strength functions, information entropy and Porter-Thomas distribution for wave function structure as generated by these ensembles are briefly discussed. In addition, presented are some aspects of data analysis. © 2014 Springer International Publishing Switzerland.