Birth of a gap: critical phenomena in the normal matrix model

We investigate a family of radially symmetric Coulomb gas systems at inverse
temperature

coming from the normal matrix model. The family is characterised by the
property that the density of the equilibrium measure vanishes on a ring at
radius , which lies strictly inside the droplet. The large n expansion of
the free energy is obtained up to a novel term. Next, we perform a scaling
limit of the correlation kernel at the scale and obtain a new limiting
kernel in the bulk, which differs from the well-known Ginibre kernel.

Joint work with Matthias Allard based on arXiv:2509.24529