Alexander E. Litvak

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20202026

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math.MG2025

Minimal dispersion on the sphere

Alexander E. Litvak, Mathias Sonnleitner, Tomasz Szczepanski

The minimal spherical cap dispersion $disp_{C} (n, d)$ is the largest number $ε \in (0, 1]$ such that, for every $n$ points on the $d$ -dimensional Euclidean u…

math.MG2024

Minimal dispersion on the cube and the torus

Andrii Arman, Alexander E. Litvak

We improve some upper bounds for minimal dispersion on the cube and torus. /Our new ingredient is an improvement of a probabilistic lemma used to obtain upper bounds for dispersion…

math.MG2020

Random section and random simplex inequality

Alexander E. Litvak, Dmitry Zaporozhets

Consider some convex body $K \subset R^{d}$ . Let $X_{1}, \dots, X_{k}$ , where $k \leq d$ , be random points independently and uniformly chosen in $K$ , and let $ξ_{k}$ be a uniformly dis…