Optimal non-gaussian Dvoretzky-Milman embeddings

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).Comment: This is part two of the paper "Structure preservation via the Wasserstein distance" (arXiv:2209.07058v1) which was split into two part