  We study the discrete-time evolution of a transformation on a set of
probability measures that is up-dated combining independently the marginals on
the atoms of partitions. This model was recently introduced in Baake, Baake and
Salamat (Discr. and contin. dynam. syst. 36, 2016) for continuous-time
evolution and generalizes previous ones based upon dyadic partitions. We
associate to the discrete-time evolution a natural Markov chain and describe
its quasi-stationary behavior retrieving all the results we recently found for
dyadic partitions.
