Optimal Non-Gaussian Dvoretzky–Milman Embeddings-Reference-Cited by-同舟云学术

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Optimal Non-Gaussian Dvoretzky–Milman Embeddings

Published:2023-11-27 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Bartl Daniel¹,Mendelson Shahar²³

Affiliation:

1. Faculty of Mathematics , University of Vienna, Vienna, 1090, Austria

2. Centre for Mathematics and Its Applications , The Australian National University, Canberra, ACT 2601, Australia

3. Department of Statistics , University of Warwick, Coventry, CV4 7AL, United Kingdom

Abstract

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).

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnad267/53828130/rnad267.pdf

Reference22 articles.

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2. Asymptotic geometric analysis, part I;Artstein-Avidan;Bull. Amer. Math. Soc. (N.S.),2015

3. A note on the largest eigenvalue of a large dimensional sample covariance matrix;Bai;J. Multivariate Anal.,1988

4. Limit of the smallest eigenvalue of a large dimensional sample covariance matrix;Bai;Ann. Prob.,1993

5. Structure preservation via the Wasserstein distance;Bartl,2022

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