Open Access
2015 Tail bounds via generic chaining
Sjoerd Dirksen
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Electron. J. Probab. 20: 1-29 (2015). DOI: 10.1214/EJP.v20-3760


We modify Talagrand's generic chaining method to obtain upper bounds for all p-th moments of the supremum of a stochastic process. These bounds lead to an estimate for the upper tail of the supremum with optimal deviation parameters. We apply our procedure to improve and extend some known deviation inequalities for suprema of unbounded empirical processes and chaos processes. As an application we give a significantly simplified proof of the restricted isometry property of the subsampled discrete Fourier transform.


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Sjoerd Dirksen. "Tail bounds via generic chaining." Electron. J. Probab. 20 1 - 29, 2015.


Accepted: 20 May 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1327.60048
MathSciNet: MR3354613
Digital Object Identifier: 10.1214/EJP.v20-3760

Keywords: chaos processes , Deviation inequalities , generic chaining , restricted isometry property , suprema of empirical processes

Vol.20 • 2015
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