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arXiv · 2309.12069

Optimal non-gaussian Dvoretzky-Milman embeddings

Daniel Bartl·Shahar Mendelson
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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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Daniel Bartl, Shahar Mendelson. 2023-09-21. Optimal non-gaussian Dvoretzky-Milman embeddings. https://arxiv.org/abs/2309.12069

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