Pierre Bizeul

activity

20192026

collaborators

11 papers

math.FA2026

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…

math.MG2026

Optimal MM* bounds for convex bodies

Pierre Bizeul

Let $K \subset R^{n}$ be a convex body in isotropic position. We prove the optimal mean-width estimate \[ M^*(K)\leq C\sqrt{n\log n}. \] The main new ingredient is a geometric inequal…

math.FA2026

Minimum Norm Interpolation via the Local Theory of Banach Spaces: The Role of $2$ -Uniform Convexity

Gil Kur, Pierre Bizeul

The minimum-norm interpolator (MNI) framework has recently attracted considerable attention as a tool for understanding generalization in overparameterized models, such as neural n…

math.MG2025

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 $n$ -dimensional convex bodies without symmetry assumptions. We prove that…

math.PR2025

Entropy and Learning of Lipschitz Functions under Log-Concave Measures

Pierre Bizeul, Boaz Klartag

We study regression of $1$ -Lipschitz functions under a log-concave measure $μ$ on $R^{d}$ . We focus on the high-dimensional regime where the sample size $n$ is subexponentia…

math.CA2025

Polynomial Approximation in $L^{2}$ of the Double Exponential via Complex Analysis

Pierre Bizeul, Boaz Klartag

We study the polynomial approximation problem in $L^{2} (μ_{1})$ where $μ_{1} (d x) = e^{- ∣ x ∣} /2 d x$ . We show that for any absolutely continuous function $f$ , $$ \sum_{k=1}^{\infty} \log^2(…

math.FA2025

The slicing conjecture via small ball estimates

Pierre Bizeul

Bourgain's slicing conjecture was recently resolved by Joseph Lehec and Bo'az Klartag. We present an alternative proof by establishing small ball probability estimates for isotropi…

math.FA2023

On the Log-Sobolev Constant of Log-Concave Vectors

Pierre Bizeul

It is well known that if a random vector satisfies a log-Sobolev inequality, all of its marginals have subgaussian tails. In the spirit of the KLS conjecture, we investigate whethe…

math.FA2022

On measures strongly log-concave on a subspace

Pierre Bizeul

In this work we study the concentration properties of log-concave measures that are curved only on a subspace of directions. Proofs uses an adapted version of the stochastic locali…

math.FA2021

Entropy and Information jump for log-concave vectors

Pierre Bizeul

We extend the result of Ball and Nguyen on the jump of entropy under convolution for logconcave random vectors. We show that the result holds for any pair of vectors (not necessari…

math.PR2019

Positive solutions for large random linear systems

Pierre Bizeul, Jamal Najim

Consider a large linear system where $A_{n}$ is a $n \times n$ matrix with independent real standard Gaussian entries, $1_{n}$ is a $n \times 1$ vector of ones and with unkn…

Presenting a proof of the Kannan-Lovasz-Simonovits conjecture

Optimal MM* bounds for convex bodies

Minimum Norm Interpolation via the Local Theory of Banach Spaces: The Role of 2-Uniform Convexity

Distances between non-symmetric convex bodies: optimal bounds up to polylog

Entropy and Learning of Lipschitz Functions under Log-Concave Measures

Polynomial Approximation in L2 of the Double Exponential via Complex Analysis

The slicing conjecture via small ball estimates

On the Log-Sobolev Constant of Log-Concave Vectors

On measures strongly log-concave on a subspace

Entropy and Information jump for log-concave vectors

Positive solutions for large random linear systems

Minimum Norm Interpolation via the Local Theory of Banach Spaces: The Role of $2$ -Uniform Convexity

Polynomial Approximation in $L^{2}$ of the Double Exponential via Complex Analysis