Length spectrum of large genus random metric maps

Abstract

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 an explicit intensity. This result extends the work of Janson and Louf to the multi-faced case.

28 pages

References in corpus (6)

• Friedman-Ramanujan functions in random hyperbolic geometry and application to spectral gaps I
• On Cheeger constants of hyperbolic surfaces
• Empirical spectral measures of quantum graphs in the Benjamini-Schramm limit
• The shapes of complementary subsurfaces to simple closed hyperbolic multi-geodesics
• Non-simple systoles on random hyperbolic surfaces for large genus
• Distances and isoperimetric inequalities in random triangulations of high genus