Tail bounds via generic chaining

Research output: Contribution to journalArticleAcademicpeer-review


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.
Original languageEnglish
Pages (from-to)1-29
JournalElectronic Journal of Probability
Issue number53
Publication statusPublished - 20 May 2015
Externally publishedYes


  • chaos processes
  • Deviation inequalities
  • generic chaining
  • restricted isometry property
  • suprema of empirical processes


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