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math.PR2023★ 1 cited
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 {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…
math.CA2023
Hole probabilities and balayage of measures for planar Coulomb gases
Christophe Charlier
We study hole probabilities of two-dimensional Coulomb gases with a general potential and arbitrary temperature. The hole region is assumed to satisfy , wh…