Daniel Bartl

activity

20232026

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math.PR2023

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 $(X, μ)$ , there is a threshold $Δ_{0}$ satisfying the following:…

math.FA2023

Optimal non-gaussian Dvoretzky-Milman embeddings

Daniel Bartl, Shahar Mendelson

We construct the first non-gaussian ensemble that yields the optimal estimate in the Dvoretzky-Milman Theorem: the ensemble exhibits almost Euclidean sections in arbitrary normed s…

math.PR2023

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…

A uniform Dvoretzky-Kiefer-Wolfowitz inequality

Optimal non-gaussian Dvoretzky-Milman embeddings

Empirical approximation of the gaussian distribution in Rd

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