Optimal non-gaussian Dvoretzky-Milman embeddings
Functional Analysis
2023-12-04 v1 Probability
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).
Cite
@article{arxiv.2309.12069,
title = {Optimal non-gaussian Dvoretzky-Milman embeddings},
author = {Daniel Bartl and Shahar Mendelson},
journal= {arXiv preprint arXiv:2309.12069},
year = {2023}
}
Comments
This is part two of the paper "Structure preservation via the Wasserstein distance" (arXiv:2209.07058v1) which was split into two parts