A Bernstein-Chernoff deviation inequality, and geometric properties of random families of operators

Shiri Artstein-Avidan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper we first describe a new deviation inequality for sums of independent random variables which uses the precise constants appearing in the tails of their distributions, and can reflect in full their concentration properties. In the proof we make use of Chernoff's bounds. We then apply this inequality to prove a global diameter reduction theorem for abstract families of linear operators endowed with a probability measure satisfying some condition. Next we give a local diameter reduction theorem for abstract families of linear operators. We discuss some examples and give one more global result in the reverse direction, and extensions.

Original languageEnglish
Pages (from-to)187-204
Number of pages18
JournalIsrael Journal of Mathematics
Volume156
DOIs
StatePublished - 2006
Externally publishedYes

Funding

FundersFunder number
Bonfils-Stanton Foundation2002-006

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