  Density distribution of cold exciton clouds generated into a strain-induced
potential well by two-photon excitation in Cu$_2$O is studied at 2 K. We find
that an anomalous spike, which can be interpreted as accumulation of the
excitons into the ground state, emerges at the potential minimum. The
accumulation can be due to stimulated scattering of cold excitons, mediated by
acoustic phonon emission. Possibility of the formation of the thermodynamic
Bose-Einstein condensate of paraexcitons has been discussed.
