Luca Leuzzi — NANOTEC-CNR Roma # The glassy random laser: replica symmetry breaking in the intensity fluctuations of laser emission spectra # The behavior of a recently introduced overlap parameter is analyzed, measuring the correlation between intensity fluctuations of waves in random media in different physical regimes, with varying amount of disorder and non-linearity. Its relationship is established to the standard Parisi overlap order parameter in the replica theory for spin-glasses. In the recently introduced complex spherical spin-glass model, describing the onset and behavior of random lasers, replica symmetry breaking in the intensity fluctuation overlap is shown to occur at high pumping or low temperature. This order parameter identifies the laser transition in random media and describes its glassy nature in terms of emission spectra data, the only data so far accessible in random laser measurements. The theoretical analysis is, eventually, compared to recent spectroscopy measurements demonstrating the validity of the theory and providing a straightforward interpretation of different spectral behaviors in different kinds of random lasers.