Evidence of an emergent pseudo-localized phase characterizing the
low-temperature replica symmetry breaking phase of the complex disordered
models for glassy light is provided in the mode-locked random laser model. A
pseudo-localized phase corresponds to a state in which the intensity of light
modes is neither equipartited among all modes nor really localized on few of
them. Such a hybrid phase has been recently characterized in other models, such
as the Discrete Non-Linear Schr\"odinger equation, just as a finite size
effect, while in the low temperature phase of the glassy random laser it seems
to be robust in the limit of large size.Comment: 11 pages, 6 figure
