Upper bounds for the L^q empirical process via generic chaining

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.

• Publication year

  2025

• Venue

  Unknown venue

• Publication date

  2025-11-09

• Fields of study

  Mathematics

• Identifiers
  arXiv 2511.06338
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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