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 $n\to \infty$.

23 pages, 9 figures

References in corpus (2)

• Poisson--Dirichlet distribution for random Belyi surfaces
• On the minimal diameter of closed hyperbolic surfaces

Cited by in corpus (5)

• A random cover of a compact hyperbolic surface has relative spectral gap $\frac{3}{16}-\epsilon$
• Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves
• Random Recursive Hypergraphs
• The Cheeger constants of random Belyi surfaces
• Silhouettes and generic properties of subgroups of the modular group