On Gaussian Marginals of Uniformly Convex Bodies
نویسنده
چکیده
We show that many uniformly convex bodies have Gaussian marginals in most directions in a strong sense, which takes into account the tails of the distributions. These include uniformly convex bodies with power type 2, and power type p > 2 with some additional type condition. In particular, all unit-balls of subspaces of Lp for 1 < p < ∞ have Gaussian marginals in this strong sense. Using the weaker Kolmogorov metric, we can extend our results to arbitrary uniformly convex bodies with power type p, for 2 ≤ p < 4. These results are obtained by putting the bodies in (surprisingly) non-isotropic positions and by a new concentration of volume observation for uniformly convex bodies.
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