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The diameter of random Belyi surfaces

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arxiv 1910.11809 v1 pith:RF3PSLAK submitted 2019-10-25 math.GT math.PR

Thomas Budzinski , Nicolas Curien , Bram Petri This is my paper · ORCID
classification math.GTmath.PR
keywords randomdiameterhyperbolicsurfacesasymptoticalongbelyibrooks
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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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  1. Random punctured hyperbolic surfaces & the Brownian sphere

    math.PR 2025-08 conditional novelty 8.0 of 10

    Random Weil-Petersson punctured spheres converge, after fourth-root rescaling, to the Brownian sphere.

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