The diameter of random Belyi surfaces

Thomas Budzinski; Nicolas Curien; Bram Petri

doi:10.2140/agt.2021.21.2929

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arXiv · 1910.11809

The diameter of random Belyi surfaces

Thomas Budzinski·Nicolas Curien·Bram Petri

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Abstract

We determine the asymptotic growth rate of the diameter of the random hyperbolic surfaces constructed by Brooks and Makover. This model consists of a uniform gluing of $2n$ hyperbolic ideal triangles along their sides followed by a compactification to get a random hyperbolic surface of genus roughly $n/2$. We show that the diameter of those random surfaces is asymptotic to $2 \log n$ in probability as $n \to \infty$.

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Thomas Budzinski, Nicolas Curien, Bram Petri. 2019-10-25. The diameter of random Belyi surfaces. https://doi.org/10.2140/agt.2021.21.2929

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