Random Trees in Hyperbolic FPP

Abstract

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 $T(\hat{I}¾,\ddot{I}‰)$ consisting of infinite random geodesics to a point $\hat{I}¾$ on the Gromov boundary $\partial G$ emerges naturally. These trees have a rich random geometry that we explore further in this paper.

28 pages, 2 figures. Submitted to the Proceedings of the International Colloquium on randomness, geometry and dynamics, 2024