On the mass function of stars growing in a flocculent medium
  Stars form in regions of very inhomogeneous densities and may have chaotic
orbital motions. This leads to a time variation of the accretion rate, which
will spread the masses over some mass range. We investigate the mass
distribution functions that arise from fluctuating accretion rates in
non-linear accretion, $\dot{m} \propto m^{\alpha}$. The distribution functions
evolve in time and develop a power law tail attached to a lognormal body, like
in numerical simulations of star formation. Small fluctuations may be modelled
by a Gaussian and develop a power-law tail $\propto m^{-\alpha}$ at the
high-mass side for $\alpha > 1$ and at the low-mass side for $\alpha < 1$.
Large fluctuations require that their distribution is strictly positive, for
example, lognormal. For positive fluctuations the mass distribution function
develops the power-law tail always at the high-mass hand side, independent of
$\alpha$ larger or smaller than unity.
  Furthermore, we discuss Bondi-Hoyle accretion in a supersonically turbulent
medium, the range of parameters for which non-linear stochastic growth could
shape the stellar initial mass function, as well as the effects of a
distribution of initial masses and growth times.
