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The Cheeger constants of random Belyi surfaces (2204.09853v2)
Published 21 Apr 2022 in math.DG, math.GT, and math.SP
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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