Geometry of infinite clusters in continuum percolation models with strong correlations

在过去的十年中，在理解具有强相关性的渗透的晶格模型方面取得了巨大的进展，无论是在特定的例子中，如随机交错，还是在一般系统中。本文的研究对象是具有长程空间相关性的连续体渗流模型。一些例子是布尔模型，布朗交错，泊松圆柱体和它们的空集。主要的焦点在于开发新的工具来解决连续体模型固有的困难。

In the last ten years tremendous progress has been achieved in understanding lattice models of percolation with strong correlations, both in particular examples such as random interlacements as well as in general systems. The objects of this research proposal are percolation models in continuum with long-range spatial correlations. Some examples are the Boolean model, the Brownian interlacements, the Poisson cylinders and their vacant sets. The main focus will lie on the development of new tools to address difficulties intrinsic to continuum models.