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Arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps
Yang Shen, Yunhui Wu · 2022-03-29 · via math.PR updates on arXiv.org

Let $\mathcal{M}_{g,n(g)}$ be the moduli space of hyperbolic surfaces of genus $g$ with $n(g)$ punctures endowed with the Weil-Petersson metric. In this paper we study the asymptotic behavior of the Cheeger constants and spectral gaps of random hyperbolic surfaces in $\mathcal{M}_{g,n(g)}$, when $n(g)$ grows slower than $g$ as $g\to \infty$.

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