4 papers
math.PR2026
Thin-shell bounds via parallel coupling
Boaz Klartag, Joseph Lehec
We prove that for any log-concave random vector in with mean zero and identity covariance, where is a universa…
math.FA2025
On the stochastic proof of the Blaschke-Santaló inequality
Joseph Lehec
In 2024, Courtade, Fathi and Mikulincer gave a proof of the symmetrized Talagrand inequality based on stochastic calculus, in the spirit of Borell's proof of the Prékopa-Leindler…
math.MG2024
Affirmative Resolution of Bourgain's Slicing Problem using Guan's Bound
Boaz Klartag, Joseph Lehec
We provide the final step in the resolution of Bourgain's slicing problem in the affirmative. Thus we establish the following theorem: for any convex body $K \subseteq \mathbb{R}^n…
math.FA2024
Isoperimetric inequalities in high-dimensional convex sets
Bo'az Klartag, Joseph Lehec
These are lecture notes focusing on recent progress towards Bourgain's slicing problem and the isoperimetric conjecture proposed by Kannan, Lovasz and Simonovits (KLS).