The galactocentric radius dependent upper mass limit of young star clusters: stochastic star formation ruled out

It is widely accepted that the distribution function of the masses of young star clusters is universal and can be purely interpreted as a probability density distribution function with a constant upper mass limit. As a result of this picture the masses of the most massive objects are exclusively determined by the size of the sample. Here we show, with very high confidence, that the masses of the most massive young star clusters in M33 decrease with increasing galactocentric radius in contradiction to the expectations from a model of a randomly sampled constant cluster mass function with a constant upper mass limit. Pure stochastic star formation is thereby ruled out. We use this example to elucidate how naive analysis of data can lead to unphysical conclusions.