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Fine Gaussian fluctuations on the Poisson space II: Rescaled kernels, marked processes and geometric U-statistics

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  • Lachièze-Rey, Raphaël
  • Peccati, Giovanni

Abstract

Continuing the analysis initiated by Lachièze-Rey and Peccati (2013), we use contraction operators to study the normal approximation of random variables having the form of a U-statistic written on the points in the support of a random Poisson measure. Applications are provided to subgraph counting, boolean models and coverage of random networks.

Suggested Citation

  • Lachièze-Rey, Raphaël & Peccati, Giovanni, 2013. "Fine Gaussian fluctuations on the Poisson space II: Rescaled kernels, marked processes and geometric U-statistics," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4186-4218.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:12:p:4186-4218
    DOI: 10.1016/j.spa.2013.06.004
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    References listed on IDEAS

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    1. Vitale, Richard A., 1992. "Covariances of symmetric statistics," Journal of Multivariate Analysis, Elsevier, vol. 41(1), pages 14-26, April.
    2. Bhattacharya, Rabi N. & Ghosh, Jayanta K., 1992. "A class of U-statistics and asymptotic normality of the number of k-clusters," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 300-330, November.
    3. Schulte, Matthias & Thäle, Christoph, 2012. "The scaling limit of Poisson-driven order statistics with applications in geometric probability," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 4096-4120.
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    Cited by:

    1. Bachmann, Sascha & Reitzner, Matthias, 2018. "Concentration for Poisson U-statistics: Subgraph counts in random geometric graphs," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3327-3352.
    2. Bachmann, Sascha, 2016. "Concentration for Poisson functionals: Component counts in random geometric graphs," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1306-1330.
    3. Matthias Schulte, 2016. "Normal Approximation of Poisson Functionals in Kolmogorov Distance," Journal of Theoretical Probability, Springer, vol. 29(1), pages 96-117, March.

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