Weizmann Logo
ECCC
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



REPORTS > DETAIL:

Paper:

TR22-091 | 2nd July 2022 13:47

Quasirandom groups enjoy interleaved mixing

RSS-Feed




TR22-091
Authors: Harm Derksen, Emanuele Viola
Publication: 2nd July 2022 13:48
Downloads: 115
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