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- W4300704965 abstract "We study the structure of infinite geodesics in the Planar Stochastic Hyperbolic Triangulations $mathbb{T}_{lambda}$, which are the hyperbolic analogs of the UIPT. We prove that these geodesics form a supercritical Galton--Watson tree with geometric offspring distribution. The tree of infinite geodesics in $mathbb{T}_{lambda}$ provides a new notion of boundary, which is a realization of the Poisson boundary. By scaling limits arguments, we also obtain a description of the tree of infinite geodesics in the hyperbolic Brownian plane. Finally, by combining our main result with a forthcoming paper, we obtain new hyperbolicity properties of $mathbb{T}_{lambda}$: it satisfies a weaker form of Gromov-hyperbolicity and admits bi-infinite geodesics." @default.
- W4300704965 created "2022-10-04" @default.
- W4300704965 creator A5037364136 @default.
- W4300704965 date "2018-04-20" @default.
- W4300704965 modified "2023-09-30" @default.
- W4300704965 title "Infinite geodesics in hyperbolic random triangulations" @default.
- W4300704965 doi "https://doi.org/10.48550/arxiv.1804.07711" @default.
- W4300704965 hasPublicationYear "2018" @default.
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