  Let $X=\Lambda\backslash\mathbb{H}$ be a Schottky surface, that is, a
conformally compact hyperbolic surface of infinite area. Let $\delta$ denote
the Hausdorff dimension of the limit set of $\Lambda$.
  We prove that for any compact subset $\mathcal{K}
\subset\{\,s\,:\,\Re(s)>\frac{\delta}{2}\,\}$, if one picks a random degree $n$
cover $X_{n}$ of $X$ uniformly at random, then with probability tending to one
as $n\to\infty$, there are no resonances of $X_{n}$ in $\mathcal{K}$ other than
those already belonging to $X$ (and with the same multiplicity). This result is
conjectured to be the optimal one for bounded frequency resonances and is
analogous to both Alon's and Friedman's conjectures for random graphs, which
are now theorems due to Friedman and Bordenave-Collins, respectively.
