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A CLT concerning critical points of random functions on a Euclidean space

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  • Nicolaescu, Liviu I.

Abstract

We prove a central limit theorem concerning the number of critical points in large cubes of an isotropic Gaussian random function on a Euclidean space.

Suggested Citation

  • Nicolaescu, Liviu I., 2017. "A CLT concerning critical points of random functions on a Euclidean space," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3412-3446.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:10:p:3412-3446
    DOI: 10.1016/j.spa.2017.02.009
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    References listed on IDEAS

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    1. Nourdin, Ivan & Peccati, Giovanni & Podolskij, Mark, 2011. "Quantitative Breuer-Major theorems," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 793-812, April.
    2. Kratz, Marie F. & León, JoséR., 1997. "Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: Crossings and extremes," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 237-252, March.
    3. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
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    Cited by:

    1. Muirhead, Stephen, 2020. "A second moment bound for critical points of planar Gaussian fields in shrinking height windows," Statistics & Probability Letters, Elsevier, vol. 160(C).
    2. Azaïs, Jean-Marc & Delmas, Céline, 2022. "Mean number and correlation function of critical points of isotropic Gaussian fields and some results on GOE random matrices," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 411-445.

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