  Applying the new tools developed in [G1], we investigate the arcsine aging
regime of the random hopping time dynamics of the REM. Our results are optimal
in several ways. They cover the full time-scale and temperature domain where
this phenomenon occurs. On this domain the limiting clock process and
associated time correlation function are explicitly constructed. Finally, all
convergence statements w.r.t. the law of the random environment are obtained in
the strongest sense possible, except perhaps on the very last scales before
equilibrium.
