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### Paper:

TR22-091 | 2nd July 2022 13:47

#### Quasirandom groups enjoy interleaved mixing

TR22-091
Authors: Harm Derksen, Emanuele Viola
Publication: 2nd July 2022 13:48
Keywords:

Abstract:

Let $G$ be a group such that any non-trivial representation has dimension
at least $d$. Let $X=(X_{1},X_{2},\ldots,X_{t})$ and $Y=(Y_{1},Y_{2},\ldots,Y_{t})$
be distributions over $G^{t}$. Suppose that $X$ is independent from
$Y$. We show that for any $g\in G$ we have
$\left|\mathbb{P}[X_{1}Y_{1}X_{2}Y_{2}\cdots X_{t}Y_{t}=g]-1/|G|\right|\le\frac{|G|^{2t-1}}{d^{t-1}}\sqrt{\mathbb{E}_{h\in G^{t}}X(h)^{2}}\sqrt{\mathbb{E}_{h\in G^{t}}Y(h)^{2}}.$
Our results generalize, improve, and simplify previous works.

ISSN 1433-8092 | Imprint