Largest gaps between zeros of stationary Gaussian processes with polynomial correlation decay converge to a Poisson point process after rescaling.
Charlier, Smallest gaps of the two-dimensional Coulomb gas,arXiv preprint arXiv:2507.23502 (2025)
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Proves that the edge scaling limit of polynomial Bergman kernels yields the error-function kernel or a new pluricomplex multivariate version in tensorized and rotationally symmetric cases, plus an edge limit for counting statistics.
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.
citing papers explorer
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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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A pluricomplex error-function kernel at the edge of polynomial Bergman kernels
Proves that the edge scaling limit of polynomial Bergman kernels yields the error-function kernel or a new pluricomplex multivariate version in tensorized and rotationally symmetric cases, plus an edge limit for counting statistics.
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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.