The mmax-Mecl relation, the IMF and IGIMF: probabilistically sampled
  functions?
  We introduce a new method to measure the dispersion of mmax values of star
clusters and show that the observed sample of mmax is inconsistent with random
sampling from an universal stellar initial mass function (IMF) at a 99.9%
confidence level. The scatter seen in the mmax-Mecl data can be mainly (76%)
understood as being the result of observational uncertainties only. The scatter
of mmax values at a given Mecl are consistent with mostly measurement
uncertainties such that the true (physical) scatter may be very small.
Additionally, new data on the local star-formation regions Taurus-Auriga and
L1641 in Orion make stochastically formed stellar populations rather unlikely.
The data are however consistent with the local IGIMF (integrated galactic
stellar initial mass function) theory according to which a stellar population
is a sum of individual star-forming events each of which is described by well
defined physical laws. Randomly sampled IMFs and henceforth scale-free star
formation seems to be in contradiction to observed reality.
