This paper is concerned with testing global null hypotheses about population mean vectors
of high-dimensional data. Current tests require either strong mixing (independence) …

Let Z be an n-dimensional Gaussian vector and let f: ℝ n→ ℝ be a convex function. We
prove that ℙ (f (Z)≤ 𝔼 f (Z)-t Var f (Z))≤ exp-ct 2, for all t> 1 where c> 0 is an absolute …

We introduce and initiate the study of new parameters associated with any norm and any log-
concave measure on ℝ n, which provide sharp distributional inequalities. In the Gaussian …

The concentration of measure phenomenon in Gauss' space states that every L-Lipschitz
map f on ℝ n satisfies γ _n\left (\left {x:| f (x)-M_f|\,\geqslant t\right\}\right)\,\leqslant 2 e^-t^ 2 2 …

We use probabilistic, topological and combinatorial methods to establish the following
deviation inequality: For any normed space X=(R n,‖⋅‖) there exists an invertible linear …

This paper considers a new bootstrap procedure to estimate the distribution of high-
dimensional $\ell_p $-statistics, ie the $\ell_p $-norms of the sum of $ n $ independent $ d …

Let $ n $ be a large integer, and let $ G $ be the standard Gaussian vector in $\mathbb {R}^
n $. Paouris, Valettas and Zinn (2015) showed that for all $ p\in [1, c\log n] $, the variance of …

Let n be a sufficiently large natural number and let B be an origin-symmetric convex body in
R n in the ℓ-position, and such that the space (R n,‖⋅‖ B) admits a 1-unconditional basis …

Alexandrov's inequalities imply that for any convex body $ A $, the sequence of intrinsic
volumes $ V_1 (A),\ldots, V_n (A) $ is non-increasing (when suitably normalized). Milman's …

We study linear images of a symmetric convex body C⊆ ℝ N under an n× N Gaussian
random matrix G, where N≥ n. Special cases include common models of Gaussian random …