function [@Abr65].

The above analytical predictions concerning the average value of the complexness factor and its probability distribution have been checked through numerical simulations of random matrices, see Figs. 1 and 2. Numerical simulations are based on the diagonalization of the effective Hamiltonian (\[heff\]) viewed as a random non-Hermitian matrix. We have considered resonances in the bulk only, *i.e.* resonances with a large number of neighbors on the left and on the right of the spectrum. This restriction is introduced to neglect the edge effects whose contribution tends to vanish as $N\rightarrow \infty$.

The picket-fence Hamiltonian is built such that the eigenenergies are equally spaced and the eigenvectors are random Gaussian variables. This is readily done by following a procedure adapted from [@Gor97] where the authors used it to generate the POE ensemble. Thus, in a basis deduced from its eigenbasis through an arbitrary orthogonal transformation $O$ with random Gaussian variables, the Hamiltonian $H$ is given by: $$H = O\,\text{diag}\{ E_n\} O^t$$ where $E_n=n/N$, such that $\Delta=1/N$, and $${\left \langle O_{ij} \right \rangle}=0, \quad
 {\left \langle O_{ij}^2 \right \rangle}=1/N$$ Statistics were performed with 100 matrices of size 1000$\times$1000. In order to make the calculated distributions insensitive to edge effects, 100 