  We introduce a generalization of the well-known random sequential addition
(RSA) process for hard spheres in $d$-dimensional Euclidean space
$\mathbb{R}^d$. We show that all of the $n$-particle correlation functions of
this nonequilibrium model, in a certain limit called the "ghost" RSA packing,
can be obtained analytically for all allowable densities and in any dimension.
This represents the first exactly solvable disordered sphere-packing model in
arbitrary dimension. The fact that the maximal density $\phi(\infty)=1/2^d$ of
the ghost RSA packing implies that there may be disordered sphere packings in
sufficiently high $d$ whose density exceeds Minkowski's lower bound for Bravais
lattices, the dominant asymptotic term of which is $1/2^d$. Indeed, we report
on a conjectural lower bound on the density whose asymptotic behavior is
controlled by $2^{-(0.77865...) d}$, thus providing the putative exponential
improvement on Minkowski's 100-year-old bound. Our results suggest that the
densest packings in sufficiently high dimensions may be disordered rather than
periodic, implying the existence of disordered classical ground states for some
continuous potentials.
