Random Trees in Hyperbolic FPP

Riddhipratim Basu; Mahan Mj

Random Trees in Hyperbolic FPP

Probability 2026-07-28 v1 Group Theory Geometric Topology

Authors: Riddhipratim Basu , Mahan Mj

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 $T(\xi,\omega)$ consisting of infinite random geodesics to a point $\xi$ on the Gromov boundary $\partial G$ emerges naturally. These trees have a rich random geometry that we explore further in this paper.

Cite

@article{arxiv.2607.25567,
  title  = {Random Trees in Hyperbolic FPP},
  author = {Riddhipratim Basu and Mahan Mj},
  journal= {arXiv preprint arXiv:2607.25567},
  year   = {2026}
}

Comments

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