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Number of critical points of a Gaussian random field: Condition for a finite variance

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  • Estrade, Anne
  • Fournier, Julie

Abstract

We study the number of points where the gradient of a stationary Gaussian random field restricted to a compact set in Rd takes a fixed value. We extend to higher dimensions the Geman condition, a sufficient condition on the covariance function under which the variance of this random variable is finite.

Suggested Citation

  • Estrade, Anne & Fournier, Julie, 2016. "Number of critical points of a Gaussian random field: Condition for a finite variance," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 94-99.
    • Handle: RePEc:eee:stapro:v:118:y:2016:i:c:p:94-99
    DOI: 10.1016/j.spl.2016.06.018
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    References listed on IDEAS

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    1. Taheriyoun, Ali Reza & Shafie, Khalil & Jozani, Mohammad Jafari, 2009. "A note on the higher moments of the Euler characteristic of the excursion sets of random fields," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1074-1082, April.
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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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    1. Taheriyoun, Ali Reza, 2012. "Testing the covariance function of stationary Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 606-613.

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