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Analysis reveals operator norm tends to zero in high-dimensional products of random Fourier-Walsh matrices, indicating polynomial scaling effects.
We consider matrix products of the form A₁(A₂A₂)^…(AₘAₘ⁾Aₘ₊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.
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Zhu et al. (2025) studied this question.
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