8 papers
Digesting the proof of the sharp thin-shell inequality
Yuansi Chen, Boaz Klartag
We present a proof that determines the optimal value of the universal constant in the thin-shell theorem for log-concave distributions in high dimensions. We prove that for any log…
Distances between non-symmetric convex bodies: optimal bounds up to polylog
Pierre Bizeul, Boaz Klartag
In this paper we determine, up to polylogarithmic factors, the diameter of the Banach--Mazur compactum of -dimensional convex bodies without symmetry assumptions. We prove that…
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…
Entropy and Learning of Lipschitz Functions under Log-Concave Measures
Pierre Bizeul, Boaz Klartag
We study regression of -Lipschitz functions under a log-concave measure on . We focus on the high-dimensional regime where the sample size is subexponenti…
Polynomial Approximation in of the Double Exponential via Complex Analysis
Pierre Bizeul, Boaz Klartag
We study the polynomial approximation problem in where . We show that for any absolutely continuous function , $$ \sum_{k=1}^{\infty} \log^…
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…