We propose an approach based on random matrix theory to calculate the temporal second-order intensity correlation function $g^{\left(2\right)}\left(t\right)$ 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 a large number of random scattering centers substantially hinder the calculation of $g^{\left(2\right)}\left(t\right)$. Here, we apply in a photonic system the universal statistical properties of Ginibre's non-Hermitian random matrix ensemble to obtain $g^{\left(2\right)}\left(t\right)$. 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.

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