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math.PR2025
Free energy and fluctuations in the random normal matrix model with spectral gaps
Yacin Ameur, Christophe Charlier, Joakim Cronvall
We study large expansions for the partition function of a Coulomb gas $$Z_n=\frac 1 {Ï^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_…
math.PR2025
Smallest gaps of the two-dimensional Coulomb gas
Christophe Charlier
We consider the two-dimensional Coulomb gas with a general potential at the determinantal temperature, or equivalently, the eigenvalues of random normal matrices. We prove that the…