We review some older and more recent results concerning the energy and
particle distribution in ground states of heavy Coulomb systems. The reviewed
results are asymptotic in nature: they describe properties of many-particle
systems in the limit of a large number of particles. Particular emphasis is put
on models that take relativistic kinematics into account. While
non-relativistic models are typically rather well understood, this is generally
not the case for relativistic ones and leads to a variety of open questions.Comment: 62 page