Antonis Tsolomitis

John's Theorem for an Arbitrary Pair of Convex Bodies

We provide a generalization of Johns representation of the identity for the maximal volume position of L inside K, where K and L are arbitrary smooth convex bodies in ℝn. From this representation we obtain Banach–Mazur distance and volume ratio estimates.

Random Points in Isotropic Unconditional Convex Bodies

The paper considers three questions about independent random points uniformly distributed in isotropic symmetric convex bodies

Quantitative Steiner/Schwarz-type symmetrizations

K, T_1,\ldots, T_s

Geometry of the _{}-centroid bodies of an isotropic log-concave measure

. (a) Let

A Direct TeX-to-Braille Transcribing Method

\varepsilon\,{\in}\, (0,1)

Functional Analysis: An Introduction

and let

Asymptotic formulas for the diameter of sections of symmetric convex bodies

x_1,\ldots, x_N

Asymptotic shape of a random polytope in a convex body

be chosen from K . Is it true that if

Volume radius of a random polytope in a convex body

N\,{\geq}\, C(\varepsilon )n\log n

Quermaßintegrals and asymptotic shape of random polytopes in an isotropic convex body

, then \[\left\| I-\frac{1}{NL_K^2}\sum_{i=1}^Nx_i\otimes x_i\right\| with probability greater than