4 papers
Empirical dual volumes
Grigoris Paouris, Peter Pivovarov, Paul Simanjuntak
We introduce an empirical version of dual volumes within dual Brunn--Minkowski theory. These provide a simple model for computation and analysis under symmetrization, including mom…
Optimal mean width and metric entropy estimates for convex bodies
Grigoris Paouris, Reese Pathak
We show that there exists a constant such that for any and any convex body , \[ 1 \leq \inf_{T \in \mathrm{GL}(n)} \, \frac{M^\ast(TK)}{\…
Can we spot a fake?
Shahar Mendelson, Grigoris Paouris, Roman Vershynin
The problem of detecting fake data inspires the following seemingly simple mathematical question. Sample a data point from the standard normal distribution in . A…
Empirical forms of the Petty projection inequality
Grigoris Paouris, Peter Pivovarov, Kateryna Tatarko
The Petty projection inequality is a fundamental affine isoperimetric principle for convex sets. It has shaped several directions of research in convex geometry which forged new co…