A symmetric random variable is called a Gaussian mixture if it has the same distribution as
the product of two independent random variables, one being positive and the other a …

Let μ be a log-concave probability measure on R n and for any N> n consider the random
polytope KN= conv {X 1,…, XN}, where X 1, X 2,… are independent random points in R n …

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 …

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 …

Although there is an extensive literature on the maxima of Gaussian processes, there are
relatively few non-asymptotic bounds on their lower-tail probabilities. The aim of this paper is …

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 …

Tail Bounds for Sums of Independent Two-Sided Exponential Random Variables |
SpringerLink Skip to main content Advertisement SpringerLink Search Go to cart Search …

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 $ Z $ be an $ n $-dimensional Gaussian vector and let $ f:\mathbb R^ n\to\mathbb R $ be
a convex function. We show that: $$\mathbb P\left (f (Z)\leq\mathbb E f (Z)-t\sqrt {{\rm Var} f …

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 …