Although these models are highly abstract that very fact enables them to form a foundation for many different fields. * In thermodynamics the Ehrenfest model (

Although these models are highly abstract that very fact enables them to form a foundation for many different fields. * In thermodynamics the Ehrenfest model (or dog-flea model) was developed: http://www.wikiwand.com/en/Ehrenfest_model http://www.wikiwand.com/en/Ehrenfest_model * In spread of infectious diseases and vaccine efficacy models Polya urn models can be used. * In exchangeable models (e.g. in classification where labels are assigned but without semantics!!) the Pitman-Yor (PY) process can be described as an urn model and exhibits power-law distribution (of items over the different classes) as well. The Pitman-Yor process is a (two-parameter) generalization of the Poisson-Dirichlet process. The "proper" distribution over the space of all partitions. The urn model for PY is as follows. Start with a black ball with weight "b". At each step sample a ball proportional to its weight. If you sample a black ball, put it back in, along with another one black ball of weight "a", plus(!) a ball of a color - sampled from a base distribution H - with weight "1-a". If you sample a colored ball, put it back in, along with a ball of the same color and weight "1". The model from Tria et al. is also a two-parameter model, but I've to check if it is indeed different. I guess it is, Strogatz rulez. ;-) Edit: paper by Teh that describes Zipf's law (proportion of tables with n customers scales as O(n^{-1-d})) and Heap's law (total number of tables with n customers scales as O(n^d)) for the PY process: http://www.stats.ox.ac.uk/~teh/research/npbayes/TehJor2010a.pdf http://www.stats.ox.ac.uk/~teh/research/npbayes/TehJor2010a....