The mmax-Mecl relation, the IMF and IGIMF: probabilistically sampled functions

We introduce a new method to measure the dispersion of m(max) values of star clusters and show that the observed sample of m(max) is inconsistent with random sampling from a universal stellar initial mass function (IMF) at a 99.9 per cent confidence level. The scatter seen in the m(max)-M-ecl data can be mainly (76 per cent) understood as being the result of observational uncertainties only. The scatter of m(max) values at a given M-ecl is consistent with mostly being 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 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.