For a general potential, the smallest gaps of the 2D Coulomb gas at beta=2 are of order n^{-3/4} and converge to a Poisson point process with intensity determined by the equilibrium density.
Smallest gaps between eigenvalues of real Gaussian matrices
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We consider an $n\times n$ matrix of independent real Gaussian random variables and determine the asymptotic distribution of the smallest gaps between complex eigenvalues.
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Smallest gaps of the two-dimensional Coulomb gas
For a general potential, the smallest gaps of the 2D Coulomb gas at beta=2 are of order n^{-3/4} and converge to a Poisson point process with intensity determined by the equilibrium density.