  We present a simple statistical analysis of recent numerical simulations
exploring the correlation between the core mass function obtained from the
fragmentation of a molecular cloud and the stellar mass function which forms
from these collapsing cores. Our analysis shows that the distributions of bound
cores and sink particles obtained in the simulations are consistent with the
sinks being formed predominantly from their parent core mass reservoir, with a
statistical dispersion of the order of one third of the core mass. Such a
characteristic dispersion suggests that the stellar initial mass function is
relatively tightly correlated to the parent core mass function, leading to two
similar distributions, as observed. This in turn argues in favor of the IMF
being essentially determined at the early stages of core formation and being
only weakly affected by the various environmental factors beyond the initial
core mass reservoir, at least in the mass range explored in the present study.
Accordingly, the final IMF of a star forming region should be determined
reasonably accurately, statistically speaking, from the initial core mass
function, provided some uniform efficiency factor. The calculations also show
that these statistical fluctuations, due e.g. to variations among the core
properties, broaden the low-mass tail of the IMF compared with the parent CMF,
providing an explanation for the fact that this latter appears to underestimate
the number of "pre brown dwarf" cores compared with the observationally-derived
brown dwarf IMF.
