标题： 高秩的泊松-沃罗诺伊渗流 显示英文标题

标题： Poisson-Voronoi percolation in higher rank

摘要： 我们证明了对于具有性质 (T) 的连通秩较高半单李群的对称空间上的泊松-沃罗诺伊渗流，其唯一性阈值在低强度极限下收敛到零。这一现象从根本上不同于之前研究泊松-沃罗诺伊渗流的情况。我们的方法基于 Fraczyk、Mellick 和 Wilkens 的近期突破（arXiv:2307.01194），并为加博里奥的固定价格问题提供了一种替代的证明策略。作为我们结果的进一步应用，我们给出了一类新的非递归凯莱图的例子，这些例子允许因子 iid 债券渗流，具有唯一的无限簇和任意小的期望度数，回答了一个由哈特克罗夫特-皮特启发的问题（《数学发明》，221卷，2020年）。 显示英文摘要

摘要： We show that the uniqueness thresholds for Poisson-Voronoi percolation in symmetric spaces of connected higher rank semisimple Lie groups with property (T) converge to zero in the low-intensity limit. This phenomenon is fundamentally different from situations in which Poisson-Voronoi percolation has previously been studied. Our approach builds on a recent breakthrough of Fraczyk, Mellick and Wilkens (arXiv:2307.01194) and provides an alternative proof strategy for Gaboriau's fixed price problem. As a further application of our result, we give a new class of examples of non-amenable Cayley graphs that admit factor of iid bond percolations with a unique infinite cluster and arbitrarily small expected degree, answering a question inspired by Hutchcroft-Pete (Invent. math. 221 (2020)).}