For 2D Coulomb gases with temperature beta between 1/N and 1/(sqrt(N) log N), the microscopic point process converges to a homogeneous Poisson point process with intensity equal to the equilibrium measure density.
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Poisson Statistics for Coulomb Gases at Intermediate Temperature Regimes
For 2D Coulomb gases with temperature beta between 1/N and 1/(sqrt(N) log N), the microscopic point process converges to a homogeneous Poisson point process with intensity equal to the equilibrium measure density.