Pierre Bizeul

activity

20192026

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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…

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

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