IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v160y2020ics0167715220300018.html
   My bibliography  Save this article

A second moment bound for critical points of planar Gaussian fields in shrinking height windows

Author

Listed:
  • Muirhead, Stephen

Abstract

We consider the number of critical points of a stationary planar Gaussian field, restricted to a large domain, whose heights lie in a certain interval. Asymptotics for the mean of this quantity are simple to establish via the Kac–Rice formula, and recently Estrade and Fournier proved a second moment bound that is optimal in the case that the height interval does not depend on the size of the domain. We establish an improved bound in the more delicate case of height windows that are shrinking with the size of the domain.

Suggested Citation

  • 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).
  • Handle: RePEc:eee:stapro:v:160:y:2020:i:c:s0167715220300018
    DOI: 10.1016/j.spl.2020.108698
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715220300018
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2020.108698?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Cammarota, V. & Wigman, I., 2017. "Fluctuations of the total number of critical points of random spherical harmonics," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3825-3869.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ladgham, Safa & Lachieze-Rey, Raphaël, 2023. "Local repulsion of planar Gaussian critical points," Stochastic Processes and their Applications, Elsevier, vol. 166(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Cammarota, Valentina & Marinucci, Domenico, 2020. "A reduction principle for the critical values of random spherical harmonics," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2433-2470.
    3. Valentina Cammarota & Domenico Marinucci, 2022. "On the Correlation of Critical Points and Angular Trispectrum for Random Spherical Harmonics," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2269-2303, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:160:y:2020:i:c:s0167715220300018. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.