论文标题
quasirandom群体喜欢交错的混合
Quasirandom groups enjoy interleaved mixing
论文作者
论文摘要
让$ g $为一个组，以使任何非平凡表示的尺寸至少$ d $。令$ x =（x_ {1}，x_ {2}，\ ldots，x_ {t}）$和$ y =（y__ {1}，y_ {2}，\ ldots，y_ {t}），y_ {t}）$ be be g g^{t} $。假设$ x $来自$ y $。我们表明，对于任何$ g \ g $中的任何$ g \，我们都有$ | \ mathbb {p} [x_ {1} y_ {1} x_ {2} y_ {2} y_ {2} \ cdots x_ {t} y_ {t} = g] -1/| g || \ le \ frac {| g |^{2t-1}}} {d^{t-r-sqrt {\ sqrt {\ mathbb {e} _} _} _ {h \ in g^{t}} x（h）^{2}} \ sqrt {\ mathbb {e} _ {h \ in g^{t}} y（t}} y（h）^{2}}}。$我们的结果总体化，改进，改进，改进和简化先前的工作。
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 $|\mathbb{P}[X_{1}Y_{1}X_{2}Y_{2}\cdots X_{t}Y_{t}=g]-1/|G||\le\frac{|G|^{2t-1}}{d^{t-1}}\sqrt{\mathbb{E}_{h\in G^{t}}X(h)^{2}}\sqrt{\mathbb{E}_{h\in G^{t}}Y(h)^{2}}.$ Our results generalize, improve, and simplify previous works.
