Fluctuations in a Diffusive Medium with Gain

We present a stochastic model for amplifying, diffusive media such as, for instance, random lasers. Starting from a simple random-walk model, we derive a stochastic partial differential equation for the energy field which contains a multiplicative random-advection term yielding intermittency and power-law distributions of the field itself. A dimensional analysis indicates that such features are more likely to be observed for small enough samples and in lower spatial dimensions.