Concentration inequalities for smooth random fields

D. Belomestny, V. Spokoiny

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper we derive a sharp concentration inequality for the supremum of a smooth random field over a finite dimensional set. It is shown that this supremum can be bounded with high probability by the value of the field at some deterministic point plus an intrinsic dimension of the optimization problem. As an application we prove the exponential inequality for a function of the maximal eigenvalue of a random matrix.

Original languageEnglish
Pages (from-to)314-323
Number of pages10
JournalTheory of Probability and its Applications
Volume58
Issue number2
DOIs
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • Concentration inequalities
  • Maximal eigenvalue of a random matrix
  • Smooth random fields

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