levels at each end of the spectrum were discarded. In all the simulations the mean spectral width is kept fixed and equal to ${\left \langle \Gamma \right \rangle}/\Delta=10^{-2}$.

The GOE model
-------------

The probability distribution in the GOE case can be found by making use of group integration methods and results obtained in [@Scho00]. Outlining the details of the computation in Appendix \[AppC\], we state the final result here: $$\label{pXgoe}
 {\mathcal{P}^{\mathrm{goe}}}_M(X)=\frac{\pi^2M}{24X^2}\frac{1+\pi^2(3+M)/(4X)}{[1+\pi^2/(4X)]^{M/2+2}}.$$

(0,0)![(Color online) The distribution of the rescaled complexness parameter for the GOE model at $M=1,5$ and 10 (top, middle and bottom, respectively). The analytical result (\[pXgoe\]) is shown in the solid line and compared to that (\[p\_M(X)int\]) of the picket-fence case (dashed line) while the histograms correspond to numerical simulations. Insets show the tail of the distribution in a log-log scale.](q_distr3.eps "fig:")

\#1\#2\#3\#4\#5[ @font ]{}

(3476,6768)(2195,-7794) (2726,-6087)[(0,0)\[rb\]]{} (2726,-5449)[(0,0)\[rb\]]{} (2731,-2963)[(0,0)\[rb\]]{} (2731,-2266)[(0,0)\[rb\]]{} (2731,-1570)[(0,0)\[rb\]]{} (4925,-2664)[(0,0)\[b\]]{} (5406,-2664)[(0,0)\[b\]]{} (3788,-2664)[(0,0)\[b\]]{} (4162,-6826)[(0,0)\[b\]]{} (4817,-6826)[(0,0)\[b\]]{} (5192,-6826)[(0,0)\[b\]]{} (5467,-6826)[(0,0)\[b\]]{} (3972,-4656)[(0,0)\[b\]]{} (4685,-4656)[(0,0)\[b\]]{} (5101,-4656)[(0,0)\[b\]]{} (5413,-4656)[(0,0)\[b\]]{} (3765,-4492)[(0,0)\[rb\]]{} (3765,-3694)[(0,0)\[rb\]]{} (3153,-7515)[(0,0)\[b\]]{} (3498,-7515)[(0,0)\[b\]]{} (3843,-7515)[(0,0)\[b\]]{} (4187,-7515)[(0,0)\[b\]]{} (4532,-7515)[(0,0)\[b\]]{} (4876,-7515)[(0,0)\[b\]]{} (5220,-7515)[(0,0)\[b\]]{} (5564,-7515)[(0,0)\[b\]]{} (2809,-7515)[(0,0)\[b\]]{} (4192,-7739)[(0,0)\[b\]]{} (3500,-5300)[(0,0)\[b\]]{} (4187,-5300)[(0,0)\[b\]]{} (4878,-5300)[(0,0)\[b\]]{} (5564,-5300)[(0,0)\[b\]]{} (2729,-5163)[(0,0)\[rb\]]{} (2729,-4399)[(0,0)\[rb\]]{} (2729,-3635)[(0,0)\[rb\]]{} (2726,-7361)[(0,0)\[rb\]]{} (2726,-6722)[(0,0)\[rb\]]{} (2383,-6348) (2813,-3092)[(0,0)\[b\]]{} (3500,-3092)[(0,0)\[b\]]{} (4189,-3092)[(0,0)\[b\]]{} (4877,-3092)[(0,0)\[b\]]{} (5565,-3092)[(0,0)\[b\]]{} (2362,-4190) (2342,-2039) (3559,-2520)[(0,0)\[rb\]]{} (3559,-1865)[(0,0)\[rb\]]{} (3559,-1210)[(0,0)\[rb\]]{} (3822,-6565)[(0,0)\[rb\]]{} (3822,-5795)[(0,0)\[rb\]]{} (2811,-5300)[(0,0)\[b\]]{}

To check our findings, the same kind of numerical simulations as in 