  Debris disks have been found primarily around intermediate and solar mass
stars (spectral types A-K), but rarely around low-mass M-type stars. This
scarcity of detections in M star surveys can be confronted with the predictions
of the steady state collisional evolution model. First, we determine the
parameters of the disk population evolved with this model and fit to the
distribution of the fractional dust luminosities measured in the surveys of A-
and FGK-type stars observed by the infrared satellite Spitzer. Thus, in our
approach, we stipulate that the initial disk mass distribution is bimodal and
that only high-mass collisionally-dominated disks are detected. The best
determined parameter is the diameter $D_c$ of the largest planetesimals in the
collisional cascade of the model, which ranges between 2 and 60 km,
consistently for disks around A- and FGK-type stars. Second, we assume that the
same disk population surrounds the M dwarfs that have been the subjects of
debris disk searches in the far-infrared with Spitzer and at submillimeter
wavelengths with radiotelescopes. We find, in the framework of our study, that
this disk population, which has been fit to the AFGK data, is still consistent
with the observed lack of disks around M dwarfs with Spitzer.
