A subgaussian embedding theorem
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.
scientific article; zbMATH DE number 5320446
scientific article