Abstract
The existence of the weak limit as n → ∞ of the uniform measure on rooted triangulations of the sphere with n vertices is proved. Some properties of the limit are studied. In particular, the limit is a probability measure on random triangulations of the plane.
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Acknowledgement
We thank Itai Benjamini and Bálint Virág for inspiring conversations. Part of this research was done during visits of the first author to Microsoft Research. The first author thanks his hosts for these visits.
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Angel, O., Schramm, O. (2011). Uniform Infinite Planar Triangulations. In: Benjamini, I., Häggström, O. (eds) Selected Works of Oded Schramm. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9675-6_16
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