  The phenomenon of random intensity patterns, for waves propagating in the
presence of disorder, is well known in optics and in mesoscopic physics. We
study this phenomenon for cold atomic gases expanding, by a diffusion process,
in a weak random potential. We show that the density-density correlation
function of the expanding gas is strongly affected by disorder and we estimate
the typical size of a speckle spot, i.e., a region of enhanced or depleted
density. Both a Fermi gas and a Bose-Einstein condensate (in a mean field
approach) are considered.
