论文标题
本地随机组
Locally Random Groups
论文作者
论文摘要
在这项工作中，我们将介绍和研究紧凑型公制组的局部随机性概念。我们证明了混合不等式以及在小球体积附加尺寸条件下局部随机组的产物结果，并提供了此类组的几个示例。特别是，这导致了满足这种混合不平等的群体的新例子。在同一背景下，我们将开发出一个小伍德 - 帕利分解，并探索其与随机步行的光谱差距的存在的联系。此外，仅在尺寸条件下，我们将证明多尺度的熵增益结果`la bourgain-gamburd and tao。
In this work, we will introduce and study the notion of local randomness for compact metric groups. We prove a mixing inequality as well as a product result for locally random groups under an additional dimension condition on the volume of small balls and provide several examples of such groups. In particular, this leads to new examples of groups satisfying such a mixing inequality. In the same context, we will develop a Littlewood-Paley decomposition and explore its connection to the existence of the spectral gap for random walks. Moreover, under the dimension condition alone, we will prove a multi-scale entropy gain result `a la Bourgain-Gamburd and Tao.
