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arXiv · 2204.09853

The Cheeger constants of random Belyi surfaces

Yang Shen·Yunhui Wu
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Abstract

Brooks and Makover developed a combinatorial model of random hyperbolic surfaces by gluing certain hyperbolic ideal triangles. In this paper we show that for any $\epsilon>0$, as the number of ideal triangles goes to infinity, a generic hyperbolic surface in Brooks-Makover's model has Cheeger constant less than $\frac{3}{2\pi}+\epsilon$.

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Yang Shen, Yunhui Wu. 2022-04-21. The Cheeger constants of random Belyi surfaces. https://doi.org/10.1093/imrn%2Frnac323

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