1 citations · 2 across the 8 of their papers we have counts for
11 papers
Revisiting the Bobkov-Chistyakov-Götze theorem on approximately Gaussian marginals
Boaz Klartag
We study one-dimensional marginals of an isotropic, log-concave probability measure in . We show that the Kolmogorov distance between a typical marginal and the stand…
Presenting a proof of the Kannan-Lovasz-Simonovits conjecture
Pierre Bizeul, Boaz Klartag, Joseph Lehec
Together with Bourgain's slicing problem and the variance conjecture, the Kannan-Lovász-Simonovits (KLS) conjecture has been a driving force for mathematical developments in high d…
A polynomial bound in Dvoretzky's theorem
Boaz Klartag, Shahar Moshe
We present a simple proof of the -Dvoretzky conjecture, which asserts that the dependence on the approximation parameter in Dvoretzky's theorem is polyno…
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…
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 subexponentia…
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…
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^2(…
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…
The strong data processing inequality under the heat flow
Bo'az Klartag, Or Ordentlich
Let and be probability distributions on , and be their evolution under the heat flow, that is, the probability distributions resulting from convolvi…
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).