Largest gaps between zeros of stationary Gaussian processes with polynomial correlation decay converge to a Poisson point process after rescaling.
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Exact universal log-asymptotics for persistence probabilities and entropic repulsion profiles of d-dimensional stationary Gaussian fields with spectral singularity of order alpha at the origin, given explicitly via capacity and equilibrium potential of the alpha-Riesz kernel.
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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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Persistence and entropic repulsion of stationary Gaussian fields with spectral singularity at the origin
Exact universal log-asymptotics for persistence probabilities and entropic repulsion profiles of d-dimensional stationary Gaussian fields with spectral singularity of order alpha at the origin, given explicitly via capacity and equilibrium potential of the alpha-Riesz kernel.