Spacing distributions for real symmetric 2 × 2 generalized Gaussian ensembles
Michael Berry, Pragya Shukla · Journal of Physics A Mathematical and Theoretical · 2009
For ensembles of 2 × 2 real symmetric matrices, the normalized spacing distributions P ( S ) form a family whose parameter space is the unit cube with coordinates determined by the means and variances of the diagonal and off-diagonal elements. The cube contains a variety of spacing distributions that are calculated analytically; they include the Wigner–Poisson transition, distributions with singularities and Gaussians. Unfolding is superfluous for 2 × 2 matrices, but it can be implemented, giving rise to a further variety of spacing distributions, some surprising.