  In [Chu12], Church used representation stability to prove that the space of
configurations of distinct unordered points in a closed manifold exhibit
rational homological stability. A second proof was also given by
Randal-Williams in [RW11] using transfer maps. We give a third proof of this
fact using localization and rational homotopy theory. This gives new insight
into the role that the rationals play in homological stability. Our methods
also yield new information about stability for torsion in the homology of
configuration spaces of points in a closed manifold.
