  The statistical distribution of levels of an integrable system is claimed to
be a Poisson distribution. In this paper, we numerically generate an ensemble
of N dimensional random diagonal matrices as a model for regular systems. We
evaluate the corresponding nearest-neighbor spacing (NNS) distribution, which
characterizes the short range correlation between levels. To characterize the
long term correlations, we evaluate the level number variance. We show that, by
increasing the size of matrices, the level spacing distribution evolves from
the Gaussian shape that characterizes ensembles of 2\times2 matrices tending to
the Poissonian as N \rightarrow \infty. The transition occurs at N \approx 20.
The number variance also shows a gradual transition towards the straight line
behavior predicted by the Poisson statistics.

Exactly Solvable and Integrable Systems;Disordered Systems and Neural Networks