75 citations · 270 across the 14 of their papers we have counts for
14 papers
Radii of Euclidean sections of -balls
Stanislaw Szarek, Pawel Wolff
The celebrated Dvoretzky theorem asserts that every -dimensional convex body admits central sections of dimension , which is nearly spherical. For many instances…
Optimal constants in concentration inequalities on the sphere and in the Gauss space
Guillaume Aubrun, Justin Jenkinson, Stanislaw J. Szarek
We show several variants of concentration inequalities on the sphere stated as subgaussian estimates with optimal constants. For a Lipschitz function, we give one-sided and two-sid…
Constructive nonlocal games with very small classical values
M. Rosicka, S. Szarek, A. Rutkowski +2
There are few explicit examples of two player nonlocal games with a large gap between classical and quantum value. One of the reasons is that estimating the classical value is usua…
Universal gaps for XOR games from estimates on tensor norm ratios
Guillaume Aubrun, Ludovico Lami, Carlos Palazuelos +2
We define and study XOR games in the framework of general probabilistic theories, which encompasses all physical models whose predictive power obeys minimal requirements. The bias…
Two proofs of Størmer's theorem
Guillaume Aubrun, Stanisław J. Szarek
The structure of the set of positivity-preserving maps between matrix algebras is notoriously difficult to describe. The notable exceptions are the results by Størmer and Woronowic…
Dvoretzky's Theorem and the Complexity of Entanglement Detection
Guillaume Aubrun, Stanislaw Szarek
The well-known Horodecki criterion asserts that a state on is entangled if and only if there exists a positive map $Φ: \mathsf{M}_d \to \mat…