  We consider a two-dimensional Coulomb gas confined to a disk when the
external potential is radially symmetric. In the presence of a hard-wall
constraint effective to change the equilibrium, the density of the equilibrium
measure acquires a singular component at the hard wall. In the determinantal
case, we study the local statistics of Coulomb particles at the hard wall and
prove that their local correlations are expressed in terms of "Laplace-type"
integrals, which appear in the context of truncated unitary matrices in the
regime of weak non-unitarity.
