Fractional exclusion statistics and the Random Matrix Boson Ensemble
  The k-body Gaussian Embedded Ensemble of Random Matrices is considered for N bosons distributed on two single-particle levels. When k = N, the ensemble is equivalent to the Gaussian Orthogonal Ensemble (GOE), and when k = 2 it corresponds to the Two-body Random Ensemble (TBRE) for bosons. It is shown that the energy spectrum leads to a rank function which is of the form of a discrete generalized beta distribution. The same distribution is obtained assuming N non-interacting quasiparticles that obey the fractional exclusion statistics introduced by Haldane two decades ago. 
Saul Hern\'andez-Quiroz, Manuel Beltr\'an, Luis Benet, Jorge Flores   and Germinal Cocho
physics.atom-ph cond-mat.stat-mech