Projections of probability distributions: A measure-theoretic Dvoretzky theorem

الأصل · EN

Many authors have studied the phenomenon of typically Gaussian marginals of high-dimensional random vectors; e.g., for a probability measure on ᵈ, under mild conditions, most one-dimensional marginals are approximately Gaussian if d is large. In earlier work, the author used entropy techniques and Stein's method to show that this phenomenon persists in the bounded-Lipschitz distance for k-dimensional marginals of d-dimensional distributions, if k=o(√(d)). In this paper, a somewhat different approach is used to show that the phenomenon persists if k<2(d)/((d)), and that this estimate is best possible.