AI 中文总结
研究格罗莫夫双曲群上首次通过渗流测地线，因合并现象出现随机树\(T(\xi,\omega)\)，核心方法是回顾已知性质并进一步探索其随机几何性质，主要贡献是对该随机树丰富性质的研究。
AI 中文摘要
我们首先回顾了在格罗莫夫双曲群\(G\)上首次通过渗流（FPP）测地线的已知性质。由于作者早期工作中建立的合并现象，一个由到格罗莫夫边界\(\partial G\)上一点\(\xi\)的无限随机测地线组成的随机树\(T(\xi,\omega)\)自然出现。本文进一步探索了这些树丰富的随机几何性质。
英文摘要
We start by surveying known properties of first passage percolation (FPP) geodesics on a Gromov-hyperbolic group $G$. Due to a coalescence phenomenon established in earlier work of the authors, a random tree $T(ξ,ω)$ consisting of infinite random geodesics to a point $ξ$ on the Gromov boundary $\partial G$ emerges naturally. These trees have a rich random geometry that we explore further in this paper.
Comments28 pages, 2 figures. Submitted to the Proceedings of the International Colloquium on randomness, geometry and dynamics, 2024
