  We address the problem of achieving an optical random laser with a cloud of
cold atoms, in which gain and scattering are provided by the same atoms. The
lasing threshold can be defined using the on-resonance optical thickness b0 as
a single critical parameter. We predict the threshold quantitatively, as well
as power and frequency of the emitted light, using two different light
transport models and the atomic polarizability of a strongly-pumped two-level
atom. We find a critical b0 on the order of 300, which is within reach of
state-of-the-art cold-atom experiments. Interestingly, we find that random
lasing can already occur in a regime of relatively low scattering.
