In this paper, we prove three fundamental types of limit theorems for the q-norm of random
vectors chosen at random in an ℓ pn-ball in high dimensions. We obtain a central limit …

Accurate estimation of tail probabilities of projections of high-dimensional probability
measures is of relevance in high-dimensional statistics and asymptotic geometric analysis …

We develop a probabilistic approach to study the volumetric and geometric properties of unit
balls B q, 1 n of finite-dimensional Lorentz sequence spaces ℓ q, 1 n. More precisely, we …

We study the precise asymptotic volume of balls in Orlicz spaces and show that the volume
of the intersection of two Orlicz balls undergoes a phase transition when the dimension of …

We survey results concerning sharp estimates on volumes of sections and projections of
certain convex bodies, mainly ℓp-balls, by and onto lower-dimensional subspaces. This …

A probabilistic representation for a class of weighted p-radial distributions, based on
mixtures of a weighted cone probability measure and a weighted uniform distribution on the …

We consider products of uniform random variables from the Stiefel manifold of orthonormal $
k $-frames in $\mathbb {R}^ n $, $ k\le n $, and random vectors from the $ n $-dimensional …

The work of Gantert, Kim, and Ramanan [Large deviations for random projections of $\ell^ p
$ balls, Ann. Probab. 45 (6B), 2017] has initiated and inspired a new direction of research in …

Sharp large deviation results of Bahadur–Ranga Rao type are provided for the q-norm of
random vectors distributed on the ${\ell _ {p}^{n}} $-ball ${\mathbb {B} _ {p}^{n}} $ according …

In this article, we present a precise deviation formula for the intersection of two Orlicz balls
generated by Orlicz functions $ V $ and $ W $. Additionally, we establish a (quantitative) …