Bosonic stimulation as a natural realization of the Pólya urn problem

The kinematics of Bose statistics for the scattering of incoming bosons into a set of non-overlapping, degenerate single-particle states, is shown to manifest a metrically non-transitive and symmetry-breaking behaviour similar to the Pólya urn problem, familiar in diverse situations ranging from population biology to economics. It is a purely statistical consequence of bosonic stimulation, which favours scattering into a state with an already higher occupation number. A possible experimental realization is suggested.