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Concentration for Poisson functionals: Component counts in random geometric graphs

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  • Bachmann, Sascha

Abstract

Upper bounds for the probabilities P(F≥EF+r) and P(F≤EF−r) are proved, where F is a certain component count associated with a random geometric graph built over a Poisson point process on Rd. The bounds for the upper tail decay exponentially, and the lower tail estimates even have a Gaussian decay.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:5:p:1306-1330
    DOI: 10.1016/j.spa.2015.11.004
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    References listed on IDEAS

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    1. 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.
    2. Bock, Hans H., 1996. "Probabilistic models in cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 5-28, November.
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    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.

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