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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.06338 |
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Table of Contents:
- Using the generic chaining method, we derive upper bounds for the \(L^q\) process of sub-Gaussian classes when \(1 \le q \le 2\), thereby resolving an open problem posed by Al-Ghattas, Chen, and Sanz-Alonso in arXiv:2502.16916. Combined with the results of arXiv:2502.16916, this yields upper bounds for the \(L^q\) process for all \(1 \le q < \infty\). We also present corollaries of this result in the geometry of Banach spaces, including high-probability bounds on the \(\ell_q\) norm diameter of random hyperplane sections of convex bodies where the subspaces are not necessarily uniformly distributed on the Grassmannian manifold and the restricted isomorphic property for \(\ell_q\) norm.