  In a recent paper (cond-mat/0506445) we derived an expression for the
replicated free energy of a liquid of hard spheres based on the HNC free energy
functional. An approximate equation of state for the glass and an estimate of
the random close packing density were obtained in d=3. Here we show that the
HNC approximation is not needed: the same expression can be obtained from the
full diagrammatic expansion of the replicated free energy. Then, we consider
the asymptotics of this expression when the space dimension d is very large. In
this limit, the entropy of the hard sphere liquid has been computed exactly.
Using this solution, we derive asymptotic expressions for the glass transition
density and for the random close packing density for hard spheres in large
space dimension.
