The Annals of Probability

Discrepancy, chaining and subgaussian processes

Shahar Mendelson

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Abstract

We show that for a typical coordinate projection of a subgaussian class of functions, the infimum over signs inf(εi) supfF|∑i=1kεif(Xi)| is asymptotically smaller than the expectation over signs as a function of the dimension k, if the canonical Gaussian process indexed by F is continuous. To that end, we establish a bound on the discrepancy of an arbitrary subset of ℝk using properties of the canonical Gaussian process the set indexes, and then obtain quantitative structural information on a typical coordinate projection of a subgaussian class.

Article information

Source
Ann. Probab., Volume 39, Number 3 (2011), 985-1026.

Dates
First available in Project Euclid: 16 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.aop/1300281730

Digital Object Identifier
doi:10.1214/10-AOP575

Mathematical Reviews number (MathSciNet)
MR2789581

Zentralblatt MATH identifier
1226.60011

Subjects
Primary: 60C05: Combinatorial probability 60G15: Gaussian processes 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Keywords
Discrepancy generic chaining

Citation

Mendelson, Shahar. Discrepancy, chaining and subgaussian processes. Ann. Probab. 39 (2011), no. 3, 985--1026. doi:10.1214/10-AOP575. https://projecteuclid.org/euclid.aop/1300281730


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