标题： 分形渗流的最新进展 显示英文标题

标题： Recent Progress on Fractal Percolation

摘要： 这是一篇关于分形渗流过程的综述论文，也称为曼德博渗流。 其目的是提供该主题更近期研究的一般性概述，同时也包括一些较经典的结果，例如与连通性性质相关的结果。 特别强调了极限集的维数理论以及超临界状态下非平凡连通分支的几何结构。 具体而言，我们证明了非平凡连通分支的阿苏阿德谱和中间维数尽管其豪斯多夫维数、盒维数和阿苏阿德维数已知是不同的，但它们都是恒等于其盒维数。 显示英文摘要

摘要： This is a survey paper about the fractal percolation process, also known as Mandelbrot percolation. It is intended to give a general breadth overview of more recent research in the topic, but also includes some of the more classical results, for example related to the connectivity properties. Particular emphasis is put on the dimension theory of the limiting set and also on the geometry of the non-trivial connected components in the supercritical regime. In particular, we show that both the Assouad spectrum and intermediate dimensions of the non-trivial connected components are constant equal to its box dimension despite its Hausdorff, box and Assouad dimensions known to being distinct.