141 citations · 238 across the 33 of their papers we have counts for
42 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 for any and any convex body , there exists such that \[ \mathrm{diam}(TK) \lesssim \sqrt{n} \mathrm{vr}(K), \…
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…
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…
Small Ball Probabilities for Simple Random Tensors
Xuehan Hu, Grigoris Paouris
We study the small ball probability of an order- simple random tensor where are independent random vecto…
Near-Optimal Estimation of Linear Functionals with Log-Concave Observation Errors
Simon Foucart, Grigoris Paouris
This note addresses the question of optimally estimating a linear functional of an object acquired through linear observations corrupted by random noise, where optimality pertains…