TR22-091 Authors: Harm Derksen, Emanuele Viola

Publication: 2nd July 2022 13:48

Downloads: 333

Keywords:

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.