  Understanding random lasing is a formidable theoretical challenge. Unlike
conventional lasers, random lasers have no resonator to trap light, they are
highly multimode with potentially strong modal interactions and they are based
on disordered gain media, where photons undergo random multiple scattering.
Interference effects notoriously modify the propagation of waves in such random
media, but their fate in the presence of nonlinearity and interactions is
poorly understood. Here, we present a semiclassical theory for multimode random
lasing in the strongly scattering regime. We show that Anderson localization, a
wave-interference effect, is not affected by the presence of nonlinearities. To
the contrary, its presence suppresses interactions between simultaneously
lasing modes. Using a recently constructed theory for complex multimode lasers,
we show analytically how Anderson localization justifies a noninteracting,
single-pole approximation. Consequently, lasing modes in a strongly scattering
random laser are given by long-lived, Anderson localized modes of the passive
cavity, whose frequency and wave profile does not vary with pumping, even in
the multi-mode regime when mode overlap spatially.
