Length spectrum of large genus random metric maps

We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichmüller theory approach. We establish that, as the genus tends to infinity, the length spectrum converges to a Poisson point process with intensity \[\lambda(\ell) = \frac{\cosh(\ell) - 1}{\ell}.\] This result extends the work of Janson and Louf to the multi-faced case.