Abstract
A random vector (X 1,… X n) is called isotropic if there exists a quasi-norm q on ℝn such that the density level curves for this vector are of the form {x : q(x) = const}. A random vector (X 1,… X n) is called pseudo-isotropic if the level curves for its characteristic function are of the form {x : c(x) = r}, r ≥ 0, for some quasi-norm c on ℝn. We discuss in the paper random vectors having both properties. We show for example that an isotropic random vector which is symmetric and stable must be sub-Gaussian.
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