Random embeddings with an almost Gaussian distortion
Advances in Mathematics(2022)
摘要
Let X be a symmetric, isotropic random vector in Rm and let X1...,Xn be independent copies of X. We show that under mild assumptions on ‖X‖2 (a suitable thin-shell bound) and on the tail-decay of the marginals 〈X,u〉, the random matrix A, whose columns are Xi/m exhibits a Gaussian-like behaviour in the following sense: for an arbitrary subset of T⊂Rn, the distortion supt∈T|‖At‖22−‖t‖22| is almost the same as if A were a Gaussian matrix.
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关键词
46B09,46N30,52A23,60G99
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