Free energy and fluctuations in the random normal matrix model with spectral gaps

Yacin Ameur, Christophe Charlier, Joakim Cronvall

We study large $n$ expansions for the partition function of a Coulomb gas $$Z_n=\frac 1 {π^n}\int_{\mathbb{C}^n}\prod_{1\le i<j\le n}|z_i-z_j|^2\prod_{i=1}^n e^{-nQ(z_i)}\, d^2 z_i…