ψ α-Estimates for Marginals of Log-Concave Probability Measures
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We show that a random marginal π F (μ) of an isotropic log-concave probability measure μ on R n exhibits better ψ α-behavior. For a natural variant ψ' α of the standard ψ α-norm we show the following: (i) If k ≤√n, then for a random F ε G n,k we have that π F (μ) is a ψ' 2- measure. We complement this result by showing that a random π F (μ) is, at the same time, super-Gaussian. (ii) If k = n δ, 1/2 < δ < 1, then for a random F ε G n,k we have that π F (μ) is a ψ' α(δ)-measure, where α(δ) = 2δ/3δ-1. © 2011 American Mathematical Society.
author list (cited authors)
Giannopoulos, A., Paouris, G., & Valettas, P.