Random Trees in Hyperbolic FPP

2026/07/28 by Riddhipratim Basu, Mahan Mj
#math.PR #math.GR #math.GT

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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(ξ,ω) consisting of infinite random geodesics to a point ξ on the Gromov boundary ∂ G emerges naturally. These trees have a rich random geometry that we explore further in this paper.

Citations

• Sublinear Morse Geodesics and First Passage Percolation
• Geodesic Trees and Exceptional Directions in FPP on Hyperbolic Groups
• Geodesic trees in last passage percolation and some related problems
• Thick trace at infinity for the Hyperbolic Radial Spanning Tree
• First Passage Percolation on Hyperbolic groups
• Cannon-Thurston Maps
• Some ergodic properties of metrics on hyperbolic groups
• Random coalescing geodesics in first-passage percolation
• First Passage percolation on a hyperbolic graph admits bi-infinite geodesics
• Multiple geodesics with the same direction
• Tightness of Fluctuations of First Passage Percolation on Some Large Graphs
• Commensurated subgroups of arithmetic groups, totally disconnected groups and adelic rigidity
• Geodesics in First Passage Percolation
• Coexistence for Richardson type competing spatial growth models

Related

• Geodesic Trees and Exceptional Directions in FPP on Hyperbolic Groups
• First Passage Percolation on Hyperbolic groups
• Infinite geodesics in hyperbolic random triangulations
• First Passage percolation on a hyperbolic graph admits bi-infinite geodesics
• Random coalescing geodesics in first-passage percolation