Uniform spectral gaps for random hyperbolic surfaces with not many cusps

Yuxin He, Yunhui Wu, Yuhao Xue

In this paper, we investigate uniform spectral gaps for Weil-Petersson random hyperbolic surfaces with not many cusps. We show that if $n=O(g^{\hat{I}}\pm )$ where $α\in \left[0,\frac{1}{2}\…