On the spectral norms of pseudo-wigner and related matrices

We investigate the spectral norms of symmetric N × N matrices from two pseudo-random ensembles. The first is the pseudo-Wigner ensemble introduced in 'Pseudo-Wigner Matrices' by Soloveychik, Xiang and Tarokh and the second is its sample covariance-Type analog defined in this work. Both ensembles are defined through the concept of r-independence by controlling the amount of randomness in the underlying matrices, and can be constructed from dual BCH codes. We show that when the measure of randomness r grows as Np, where p (0,1] and ϵ > 0, the norm of the matrices is almost surely within o(log1 + ϵN/Nmin[ρ, 2/3]) distance from 1. Numerical simulations verifying the obtained results are provided.

Duke Scholars

Author Vahid Tarokh Electrical and Computer Engineering