IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v26y2013i2d10.1007_s10959-012-0437-0.html
   My bibliography  Save this article

Moderate Deviations via Cumulants

Author

Listed:
  • Hanna Döring

    (Technische Universität Berlin)

  • Peter Eichelsbacher

    (Ruhr-Universität Bochum)

Abstract

The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations probabilities due to Rudzkis, Saulis, and Statulevičius. The examples of random objects we treat include dependency graphs, subgraph-counting statistics in Erdös–Rényi random graphs and U-statistics. Moreover, we prove moderate deviation principles for certain statistics appearing in random matrix theory, namely characteristic polynomials of random unitary matrices and the number of particles in a growing box of random determinantal point processes such as the number of eigenvalues in the GUE or the number of points in Airy, Bessel, and sine random point fields.

Suggested Citation

  • Hanna Döring & Peter Eichelsbacher, 2013. "Moderate Deviations via Cumulants," Journal of Theoretical Probability, Springer, vol. 26(2), pages 360-385, June.
    • Handle: RePEc:spr:jotpro:v:26:y:2013:i:2:d:10.1007_s10959-012-0437-0
    DOI: 10.1007/s10959-012-0437-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-012-0437-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-012-0437-0?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. Deli Li & Andrew Rosalsky, 2004. "Precise lim sup behavior of probabilities of large deviations for sums of i.i.d. random variables," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-12, January.
    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. Hafouta, Yeor, 2023. "Convergence rates in the functional CLT for α-mixing triangular arrays," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 242-290.
    2. Peter Eichelsbacher & Matthias Löwe, 2019. "Lindeberg’s Method for Moderate Deviations and Random Summation," Journal of Theoretical Probability, Springer, vol. 32(2), pages 872-897, June.
    3. Deng Zhang, 2019. "Gaussian Fluctuations and Moderate Deviations of Eigenvalues in Unitary Invariant Ensembles," Journal of Theoretical Probability, Springer, vol. 32(4), pages 1647-1687, December.
    4. Nicolas Privault, 2024. "Asymptotic Analysis of k-Hop Connectivity in the 1D Unit Disk Random Graph Model," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-26, December.
    5. Deng Zhang, 2017. "Tridiagonal Random Matrix: Gaussian Fluctuations and Deviations," Journal of Theoretical Probability, Springer, vol. 30(3), pages 1076-1103, September.
    6. Aurelija Kasparavičiūtė & Dovilė Deltuvienė, 2017. "Asymptotic Expansion for the Distribution Density Function of the Compound Poisson Process in Large Deviations," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1655-1676, December.

    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.

      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:spr:jotpro:v:26:y:2013:i:2:d:10.1007_s10959-012-0437-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

      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.