On the submultiplicativity of matrix norms induced by random vectors

In a recent two-part series of articles, A. A. Chavez, S. R. Garcia and J. Hurley [Canad. Math. Bull. 66 (2023), no. 3, 808–826; MR4651637; Canad.Math. Bull. 67 (2024), no. 2, 447–457; MR4751519] introduced a family of norms on the space Mn of n times n complex matrices that are induced by real-valued random vectors whose entries are independent and identically distributed (iid) random variables having finite d-moments where d satisfies d greater or equal to 2. These norms arise from a probabilistic framework, and their construction and validation involve probability theory, partition combinatorics, and trace polynomials in noncommuting variables.