Sharp concentration of simple random tensors II: asymmetry
Abstract
Abstract This paper establishes sharp concentration inequalities for simple random tensors. Our theory unveils a phenomenon that arises only for asymmetric tensors of order $p \ge 3$: when the effective ranks of the covariances of the component random variables lie on both sides of a critical threshold, an additional logarithmic factor emerges that is not present in sharp bounds for symmetric tensors. To establish our results, we develop empirical process theory for products of $p$ different function classes evaluated at $p$ different random variables, extending generic chaining techniques for quadratic and product empirical processes to higher-order settings.
Fields of Study & Subjects
Computational Physics and Python Applications
Advanced Mathematical Theories and Applications
Tensor decomposition and applications
Publication details
- Journal / source
- Information and Inference A Journal of the IMA
- Publisher
- Oxford University Press (OUP)
- Volume
- 15
- Issue
- 2
- Publication date
- 27 March 2026
- Language
- EN