  We consider in this note a class of two-dimensional determinantal Coulomb
gases confined by a radial external field. As the number of particles tends to
infinity, their empirical distribution tends to a probability measure supported
in a centered ring of the complex plane. A quadratic confinement corresponds to
the complex Ginibre Ensemble. In this case, it is also already known that the
asymptotic fluctuation of the radial edge follows a Gumbel law. We establish in
this note the universality of this edge behavior, beyond the quadratic case.
The approach, inspired by earlier works of Kostlan and Rider, boils down to
identities in law and to an instance of the Laplace method.
