  Random lasers are unique systems where lasing occurs due to repetitive
scattering in a disordered nanostructure. Previous descriptions of random
lasing are numerous, however a full time-dependent theory that describes the
introduction of gain directly from first principles is lacking in the
literature. This letter will present an analytic self-consistent time-dependent
theory of random lasing that contains the results from the well-known
steady-state ab-initio laser theory. This theory can also describe a number of
temporal phenomena that have been observed in previous experiments and
facilitates the incorporation of these devices into their envisioned practical
applications.
