Gaussian Orthogonal Ensemble

introduction

• The Gaussian orthogonal ensemble GOE(n) is described by the Gaussian measure with density

\[ \frac{1}{Z_{\text{GOE}(n)}} e^{- \frac{n}{4} \mathrm{tr} H^2} \] on the space of $n\times n$ real symmetric matrices $H=(H_{ij})$

• Its distribution is invariant under orthogonal conjugation, and it models Hamiltonians with time-reversal symmetry

computational resource

• https://drive.google.com/file/d/0B8XXo8Tve1cxZEdFLUVsM0hwUWM/view