Edge behavior of two-dimensional Coulomb gases near a hard wall

Abstract

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.