  We propose a new approach based on random matrix theory to calculate the
temporal second-order intensity correlation function $g^{(2)}(t)$ of the
radiation emitted by random lasers and random fiber lasers. The multimode
character of these systems, with a relevant degree of disorder in the active
medium, and large number of random scattering centers substantially hinder the
calculation of $g^{(2)}(t)$. Here we apply for the first time in a photonic
system the universal statistical properties of Ginibre's non-Hermitian random
matrix ensemble to obtain $g^{(2)}(t)$. Excellent agreement is found with
time-resolved measurements for several excitation powers of an erbium-based
random fiber laser. We also discuss the extension of the random matrix approach
to address the statistical properties of general disordered photonic systems
with various Hamiltonian symmetries.
