Optimal Non-Gaussian Dvoretzky–Milman Embeddings (2024)

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Daniel Bartl

Faculty of Mathematics

, University of Vienna, Vienna, 1090,

Austria

Corresponding author: Daniel Bartl. Email: daniel.bartl@univie.ac.at

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Shahar Mendelson

Centre for Mathematics and Its Applications

, The Australian National University, Canberra, ACT 2601,

Australia

Department of Statistics

, University of Warwick, Coventry, CV4 7AL, United Kingdom

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International Mathematics Research Notices, Volume 2024, Issue 10, May 2024, Pages 8459–8480, https://doi.org/10.1093/imrn/rnad267

Published:

27 November 2023

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    Daniel Bartl, Shahar Mendelson, Optimal Non-Gaussian Dvoretzky–Milman Embeddings, International Mathematics Research Notices, Volume 2024, Issue 10, May 2024, Pages 8459–8480, https://doi.org/10.1093/imrn/rnad267

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Abstract

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 spaces of the same dimension as the gaussian embedding—despite being very far from gaussian (in fact, it happens to be heavy-tailed).

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