Correlation between eigenvalues of random matrices

The so-called ''Legendre'' ensemble of random matrices is studied for the nontrivial case β=1 and 4. As for the more trivial case β=2 the level density has a behaviour in qualitative agreement with nuclear and atomic densities, i.e. it is concave upward and rises rapidly. The nearest neighbour spacing distributions are obtained for β=1,4; they are the same as for the Gaussian and circular ensembles