  Through a Metropolis-like algorithm with single step computational cost of
order one, we build a Markov chain that relaxes to the canonical Fermi
statistics for k non-interacting particles among m energy levels. Uniformly
over the temperature as well as the energy values and degeneracies of the
energy levels we give an explicit upper bound with leading term km(ln k) for
the mixing time of the dynamics. We obtain such construction and upper bound as
a special case of a general result on (non-homogeneous) products of ultra
log-concave measures (like binomial or Poisson laws) with a global constraint.
As a consequence of this general result we also obtain a disorder-independent
upper bound on the mixing time of a simple exclusion process on the complete
graph with site disorder. This general result is based on an elementary
coupling argument and extended to (non-homogeneous) products of log-concave
measures.
