A subgaussian embedding theorem
type: Item
instance of: scholarly article
title: A subgaussian embedding theorem
zbMATH Open document ID: 1183.46010
author: Shahar Mendelson
author: Nicole Tomczak-Jaegermann
published in: Israel Journal of Mathematics
publication date: 2008-09-03T00:00:00Z
review text: One of the consequences of the Gaussian min-max theorem proved by \textit{Y.\,Gordon} [Isr.\ J.\ Math.\ 50, 265--289 (1985; Zbl 0663.60034)] states that a subset of the Euclidean sphere can be almost isometrically embedded into a normed space using a Gaussian matrix [see also \textit{G.\,Schechtman}, Adv.\ Math.\ 200, 125--135 (2006, Zbl 1108.46011)]. In the present paper, the authors extend this result to the case of a subgaussian operator under cotype conditions on the normed space. The subgaussian operator here is a matrix whose rows are subgaussian isotropic random vectors. The new result is an isomorphic one, i.e., the constants of embedding cannot be taken close to one. Relations between corresponding parameters are provided. An application to the case of Bernoulli matrices is given.
Mathematics Subject Classification ID: 46B09
Mathematics Subject Classification ID: 52A21
Mathematics Subject Classification ID: 46B07
zbMATH DE Number: 5320446
zbMATH Keywords: cotype
zbMATH Keywords: concentration
zbMATH Keywords: Gaussian matrix
zbMATH Keywords: generic chaining
zbMATH Keywords: isotropic random vector
zbMATH Keywords: random embedding
zbMATH Keywords: subgaussian operator
zbMATH Keywords: subgaussian random vector
MaRDI profile type: Publication
full work available at URL: s11856-008-0034-1
OpenAlex ID: W1993360063
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DOI: 10.1007/S11856-008-0034-1
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description: scientific article; zbMATH DE number 5320446