Random Euclidean embeddings in finite dimensional Lorentz spaces

TL;DR

This paper provides quantitative bounds for random embeddings of finite-dimensional Euclidean spaces into Lorentz sequence spaces, improving the dependence on the approximation parameter epsilon.

Contribution

It introduces new bounds for random embeddings into Lorentz spaces with better epsilon dependence than previous results.

Findings

Improved bounds for embeddings into Lorentz spaces

Enhanced epsilon dependence in embedding estimates

Theoretical analysis of random embedding properties

Abstract

Quantitative bounds for random embeddings of $\mathbb{R}^{k}$ into Lorentz sequence spaces are given, with improved dependence on $\varepsilon$.