Quasirandom groups enjoy interleaved mixing

2022/06/19 by Derksen, Harm, Viola, Emanuele
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2206.10603

Abstract

Let G be a group such that any non-trivial representation has dimension at least d. Let X=(X₁,X₂,…,X_t) and Y=(Y₁,Y₂,…,Y_t) be distributions over G^t. Suppose that X is independent from Y. We show that for any g∈ G we have |ℙ[X₁Y₁X₂Y₂⋯ X_tY_t=g]-1/|G||≤\frac|G|^2t-1d^t-1√𝔼_{h∈ G^t}X(h)²√𝔼_{h∈ G^t}Y(h)². Our results generalize, improve, and simplify previous works.

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