Dvoretzky Type Theorems for Subgaussian Coordinate Projections

Shahar Mendelson

doi:10.1007/s10959-015-0624-x

Dvoretzky Type Theorems for Subgaussian Coordinate Projections

Shahar Mendelson^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Given a class of functions F on a probability space (Ω , μ) , we study the structure of a typical coordinate projection of the class, defined by {(f(Xi))i=1N:f∈F}, where X₁, … , X_N are independent, selected according to μ. We show that when F is a subgaussian class, a typical coordinate projection satisfies a Dvoretzky type theorem.

Original language	English
Pages (from-to)	1644-1660
Number of pages	17
Journal	Journal of Theoretical Probability
Volume	29
Issue number	4
DOIs	https://doi.org/10.1007/s10959-015-0624-x
Publication status	Published - 1 Dec 2016
Externally published	Yes

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title = "Dvoretzky Type Theorems for Subgaussian Coordinate Projections",

abstract = "Given a class of functions F on a probability space (Ω , μ) , we study the structure of a typical coordinate projection of the class, defined by \{(f(Xi))i=1N:f∈F\}, where X1, … , XN are independent, selected according to μ. We show that when F is a subgaussian class, a typical coordinate projection satisfies a Dvoretzky type theorem.",

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AB - Given a class of functions F on a probability space (Ω , μ) , we study the structure of a typical coordinate projection of the class, defined by {(f(Xi))i=1N:f∈F}, where X1, … , XN are independent, selected according to μ. We show that when F is a subgaussian class, a typical coordinate projection satisfies a Dvoretzky type theorem.

KW - Dvoretzky type theorems

KW - Empirical processes

KW - Subgaussian classes

UR - https://www.scopus.com/pages/publications/84933056699

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DO - 10.1007/s10959-015-0624-x

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EP - 1660

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

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ER -

Dvoretzky Type Theorems for Subgaussian Coordinate Projections

Abstract

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