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Some superconcentration inequalities for extrema of stationary Gaussian processes

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  • Tanguy, Kevin

Abstract

This note is concerned with concentration inequalities for extrema of stationary Gaussian processes. It provides non-asymptotic tail inequalities which fully reflect the fluctuation rate, and as such improve upon standard Gaussian concentration. The arguments rely on the hypercontractive approach developed by Chatterjee for superconcentration variance bounds. Some statistical illustrations complete the exposition.

Suggested Citation

  • Tanguy, Kevin, 2015. "Some superconcentration inequalities for extrema of stationary Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 239-246.
    • Handle: RePEc:eee:stapro:v:106:y:2015:i:c:p:239-246
    DOI: 10.1016/j.spl.2015.07.028
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    Cited by:

    1. Mordant, Gilles & Segers, Johan, 2021. "Maxima and near-maxima of a Gaussian random assignment field," Statistics & Probability Letters, Elsevier, vol. 173(C).
    2. Mordant, Gilles & Segers, Johan, 2021. "Maxima and near-maxima of a Gaussian random assignment field," LIDAM Discussion Papers ISBA 2021008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Paouris, Grigoris & Valettas, Petros & Zinn, Joel, 2017. "Random version of Dvoretzky’s theorem in ℓpn," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3187-3227.
    4. Kevin Tanguy, 2020. "Talagrand Inequality at Second Order and Application to Boolean Analysis," Journal of Theoretical Probability, Springer, vol. 33(2), pages 692-714, June.

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