  We investigate the shape of the spectrum and the spectral fluctuations of the
$k$-body Embedded Gaussian Ensemble for Bosons in the dense limit, where the
number of Bosons $m \to \infty$ while both $k$, the rank of the interaction,
and $l$, the number of single-particle states, are kept fixed. We show that the
relative fluctuations of the low spectral moments do not vanish in this limit,
proving that the ensemble is non-ergodic. Numerical simulations yield spectra
which display a strong tendency towards picket-fence type. The wave functions
also deviate from canonical random-matrix behaviour
