. For N = 2
we have exact analytic results
recently published by Grossmann and Robnik, whilst for N =
we have the theory first initiated by Brezin and Zee, and
generalized by Hackenbroich and Weidenmüller (BZHW), stating that
the local spectral fluctuations (after spectral unfolding) are
described exactly by the GOE of the random matrix theory, provided
the limiting distribution of the eigenvalues is smooth and confined
to a finite interval. We show numerically that such a transition
to the universal behaviour according to BZHW is pretty fast, and that
it does not occur if the second assumption in their theory
is not satisfied. We do this for the box (uniform) distribution and
the exponential distribution, where the conditions are satisfied
and BZHW behaviour is observed. For the two cases of the Cauchy-Lorentz and
the singular (power law times exponential) matrix element
distribution functions the second BZHW condition is not satisfied and we
indeed see that the level spacing distributions in the limit
N = do not behave like the GOE model.
Key words: random matrix theories, non-Gaussian ensembles, level spacings distribution, quantum and classical chaos
