Largest gaps between zeros of stationary Gaussian processes with polynomial correlation decay converge to a Poisson point process after rescaling.
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For random normal matrices, the scaled variance of eigenvalue count in an interior Borel set A converges to a boundary integral of sqrt(ΔQ) with respect to Hausdorff measure; a similar result holds near the droplet edge using harmonic measure.
A new flowing matrix model shows numerically that the Single Ring Theorem breaks at a critical flow parameter toward normality, while singular-value spacing statistics shift from Wigner-Dyson to Poissonian.
Derives explicit free energy expansion including constant term for determinantal Coulomb gases in quadratic fields with point charge, equating the constant to the Liouville action associated with the droplet.
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Poisson approximation of the largest gaps between zeros of a stationary Gaussian process
Largest gaps between zeros of stationary Gaussian processes with polynomial correlation decay converge to a Poisson point process after rescaling.
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Universality for fluctuations of counting statistics of random normal matrices
For random normal matrices, the scaled variance of eigenvalue count in an interior Borel set A converges to a boundary integral of sqrt(ΔQ) with respect to Hausdorff measure; a similar result holds near the droplet edge using harmonic measure.
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