The Cheeger constants of random Belyi surfaces

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 $\frac{3}{2\pi }+\epsilon$.

International Mathematics Research Notices (IMRN), to appear

References in corpus (5)

• Poisson--Dirichlet distribution for random Belyi surfaces
• Random hyperbolic surfaces of large genus have first eigenvalues greater than $\frac{3}{16}-\epsilon$
• Towards optimal spectral gaps in large genus
• Near optimal spectral gaps for hyperbolic surfaces
• On Cheeger constants of hyperbolic surfaces