Zeros of smooth stationary Gaussian processes

DOI10.1214/21-EJP637zbMath1469.60071arXiv2007.03240OpenAlexW3161538937MaRDI QIDQ2042874

Thomas Letendre, Michele Ancona

Publication date: 21 July 2021

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.03240

zbMATH Keywords

clusteringGaussian processlaw of large numberscentral limit theoremKac-Rice formulacentral moments\(k\)-point function

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

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Variance of the number of zeros of dependent Gaussian trigonometric polynomials ⋮ An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process ⋮ Functional convergence of Berry's nodal lengths: approximate tightness and total disorder ⋮ Cumulants asymptotics for the zeros counting measure of real Gaussian processes ⋮ On the finiteness of the moments of the measure of level sets of random fields ⋮ Roots of Kostlan polynomials: moments, strong law of large numbers and central limit theorem ⋮ Variance linearity for real Gaussian zeros

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