# The diameter of random Belyi surfaces

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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https://hal-universite-paris-saclay.archives-ouvertes.fr/hal-03287264
Contributor : Nicolas Curien Connect in order to contact the contributor
Submitted on : Thursday, July 15, 2021 - 3:03:54 PM
Last modification on : Saturday, July 17, 2021 - 3:46:03 AM

### Identifiers

• HAL Id : hal-03287264, version 1
• ARXIV : 1910.11809

### Citation

Thomas Budzinski, Nicolas Curien, Bram Petri. The diameter of random Belyi surfaces. 2021. ⟨hal-03287264⟩

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