Spectral norm bound for the product of random Fourier-Walsh matrices

Key Points

The operator norm approaches zero as dimensions increase, highlighting a significant scaling behavior.
Analysis of matrix products demonstrates interesting properties of random Fourier-Walsh matrices in high dimensions.
Focused on products of normalized random Fourier-Walsh matrices, leading to key theoretical insights.
Implications suggest further exploration of scaling phenomena in random matrix theory and applications.

Abstract

We consider matrix products of the form A₁ (A₂A₂) ^ (A₌A₌^) A₌+₁, where Aᵢ are normalized random Fourier-Walsh matrices. We identify an interesting polynomial scaling regime when the operator norm of the expected matrix product tends to zero as the dimension tends to infinity.

Spectral norm bound for the product of random Fourier-Walsh matrices

Key Points

Abstract

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