A random cover of a compact hyperbolic surface has relative spectral gap $\frac{3}{16}-\epsilon$

Michael Magee, Frédéric Naud, Doron Puder

Let $X$ be a compact connected hyperbolic surface, that is, a closed connected orientable smooth surface with a Riemannian metric of constant curvature -1. For each $n\in\mathbf{N}…