S. Mendelson

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20242026

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math.PR2026

On the structure of marginals in high dimensions

Daniel Bartl, Shahar Mendelson

Let $G, G_{1}, \dots, G_{N}$ be independent copies of a standard gaussian random vector in $R^{d}$ and denote by $I^ = \sum_{i = 1}^{N} ⟨ G_{i}, \cdot ⟩ e_{i}$ the standard gauss…

math.PR2026

Uniform mean estimation via generic chaining

Daniel Bartl, Shahar Mendelson

We introduce an empirical functional $I^¨$ that is an optimal uniform mean estimator: Let $F \subset L_{2} (I^¼)$ be a class of mean zero functions, $u$ is a real valued function, and $X…

math.PR2025

A uniform Dvoretzky-Kiefer-Wolfowitz inequality

Daniel Bartl, Shahar Mendelson

We show that under minimal assumptions on a class of functions $H$ defined on a probability space $(X, I^¼)$ , there is a threshold $I^_{0}$ satisfying the following…

math.PR2024

Empirical approximation of the gaussian distribution in $R^{d}$

Daniel Bartl, Shahar Mendelson

Let $G_{1}, \dots, G_{m}$ be independent copies of the standard gaussian random vector in $R^{d}$ . We show that there is an absolute constant $c$ such that for any $A \subset S^{d…

math.PR2024

Fitting an ellipsoid to a quadratic number of random points

Afonso S. Bandeira, Antoine Maillard, Shahar Mendelson +1

We consider the problem $(P)$ of fitting $n$ standard Gaussian random vectors in $R^{d}$ to the boundary of a centered ellipsoid, as $n, d \to \infty$ . This problem…

On the structure of marginals in high dimensions

Uniform mean estimation via generic chaining

A uniform Dvoretzky-Kiefer-Wolfowitz inequality

Empirical approximation of the gaussian distribution in Rd

Fitting an ellipsoid to a quadratic number of random points

Empirical approximation of the gaussian distribution in $R^{d}$