Operator ℓ∞→ℓ∞ norm of products of random matrices with iid entries
Abstract
We study the ℓ∞→ℓ∞ operator norm of products of independent random matrices with independent and identically distributed entries. For n-by-n matrices whose entries are centered, have unit variance, and have a finite moment of order 4α for some α>1, we find that the operator norm of the product of p matrices behaves asymptotically like np+1 2 2∕π. The case of products of possibly non-square matrices with possibly non-centered entries is also covered.
Fields of Study & Subjects
Random Matrices and Applications
Matrix Theory and Algorithms
Probability and Statistical Research
Publication details
- Journal / source
- Electronic Journal of Probability
- Volume
- 31
- Issue
- none
- Pages
- 1–26
- Publication date
- 1 January 2026